- An immersed submanifold of a manifold M is the image S of an immersion map f: N → M; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) - it can have self-intersections. More narrowly, one can require that the map f: N → M be an injection (one-to-one), in which we call it an injective immersion, and define an immersed.
- In any case, I don't think you'll be able to do anything with your immersed submanifold unless you have the map. My answers to the specific questions of the original poster: 1) Union of countably many submanifolds is an immersed submanifolds iff you consider a disjoint union of countably many abstract manifolds a manifold. Note that for embedded submanifolds, it's always possible to construct.
- Immersed submanifold: lt;p|>In |mathematics|, a |submanifold| of a |manifold| |M| is a |subset| |S| which itself has th... World Heritage Encyclopedia, the.

Immersions, submersions and critical values De nition 0.2 (Submersion and Immersion) If f: X!Y is smooth, then 1. If T pfis onto for all p2X, then fis called a submersion 2. If T pfis one-to-one for all p2X, then fis called a immersion 3. If fis an immersion and fis one-to-one, then f(X) is an immersed submanifold Claim: an immersed submanifold is not an embedded submanifold if and only if its manifold topology does not agree with the subspace topology.. Why I suspect the claim is true: the inclusion map is always injective by definition.Also, since it is a restriction of the identity, its derivative everywhere is just the identity transformation, and thus clearly injective

- Immersed submanifold with the subspace topology is not an embedded submanifold. In fact, when we consider the underlying set of an immersed submanifold with the subspace topology, the resulting space need not be a manifold at all. For example, with the subspace topology, the figure-eight is not a manifold since you cannot find an open set in $\mathbb{R}^2$ such that its intersection with the.
- Nis called a submanifold (or sometimes a regular submanifold ), if it is an immersive submanifold and in addition N is a topological subspace of M, i.e., if the natural manifold topology of N is the trace topology of the natural manifold topology on M. This deﬁnition is a natural generalization of the notion of submanifold of Rn, cf. [3, 2.1.5]
- This relationshipwillbestudied inChapter 6***(immersed submanifold). For the notion \Nis a submanifold of M, we require that Ninherits its di erential structure from M. Some authors refer to this relationship as \embedded submanifold. We give the de nition of submanifold in De nition 3.2***. At rst glance, it may appea
- So in particular, an immersed submanifold is a smooth manifold by itself. However, as we have seen above, globally the topology of an immersed submanifold could be di erent from the relative topology. A second way to construct smooth submanifold is to realize a submanifold as the level set of a smooth map. De nition 2.4. A smooth map f : M !N is submersion at pif the tangent map df p: T pM!T f.
- Definition 1: Immersed Submanifold Let be manifolds such that . The manifold is called an immersed submanifold of if the inclusion map is an immersion. I think you remember the meaning of immersion. And we have proved that a mapping is an immersion if there exists a canonical representation . So you could understand that for every two points and , obviously they preserve the same properties.
- An injectively immersed submanifold that is not an embedding. If M is compact, an injective immersion is an embedding, but if M is not compact then injective immersions need not be embeddings; compare to continuous bijections versus homeomorphisms. Regular homotopy. A regular homotopy between two immersions f and g from a manifold M to a manifold N is defined to be a differentiable function H.
- Eine immersierte Mannigfaltigkeit oder immersierte Untermannigfaltigkeit ist ein Objekt aus dem mathematischen Teilgebiet der Differentialtopologie.Seltener wird dieses Objekt auch immergierte Mannigfaltigkeit genannt, im Englischen spricht man meistens von einer immersed submanifold.. Hat man eine differenzierbare Abbildung: → zwischen zwei Mannigfaltigkeiten, so ist das Bild () im.

* The geometry of immersed manifolds is a generalization of the classical differential geometry of surfaces in the Euclidean space $ \mathbf R ^ {3} $*. The intrinsic and extrinsic geometries of an immersed manifold are usually described locally by means of the first and the second fundamental form, respectively. For immersions of an $ m $- dimensional manifold $ M ^ {m} $ in a manifold $ N ^ {n. Математика: погружённое подмногообрази Next, we introduce a more general kind of submanifolds, called immersed submanifolds, which turn out to be the images of injective immersions. At the end of the chapter, we show how the theory of submanifolds can be generalized to the case of submanifolds with boundary

Under suitable hypothesis, we are able to prove that such a spacelike submanifold is immersed into a slice of the ambient space. For this, we use three main core concepts: the well known generalized maximum principle of Omori and Yau, stochastic completeness and another appropriate maximum principle at infinity due to Yau. We also construct a nontrivial example of weakly trapped submanifold in. Formal Definition - Immersed SubmanifoldsAn immersed manifold of a manifold M is the image S of an immersion map f N → M in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one in which we call it an injective immersion, and define an immersed submanifold to be the image subset S together with a topology and differential. submanifold of dimension 1 of R2. In fact no connected neighborhood of p can be homeomorphic to an interval of Rminus a point. Note that fis not a homeomorphism onto its image. 1.1.3 Exercise Prove that the graph of a smooth map f : U → Rk, where U⊂ Rnis open, is a submanifold of dimension nof Rn+k. 1.1.4 Exercise Let f, g: (0,2π) → R2. <p>[3, 2.1.5]. </p> <p>also Interior geometry) of submanifolds in a Euclidean or Riemannian space.The geometry of immersed manifolds is a generalization of the classical differential geometry of surfaces in the Euclidean space $ \\mathbf R ^ {3} $. Featured on Meta An immersed submanifold of M is a subset S⊆M endowed with a topology (not necessarily the subspace topology) with respect to.

An immersed submanifold M in a Riemannian manifold N is said to be properly immersed if the immersion is a proper map. K. Akutagawa and the author gave an aﬃrmative partial answer to Conjecture 1 (Conjecture 2 particularly) as follows (cf. [2], [23]): Theorem 1.1 ([2]). Any biharmonic properly immersed submanifold in En is min-imal. For Conjecture 3, we consider a biharmonic properly. мат. погружённое подмногообрази Submanifold Last updated February 25, 2019 Immersed manifold straight line with self-intersections. In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required Let M be an immersed submanifold of a Euclidean space Em. Let 0=λ_0<λ_1<λ_2<⋯ be the eigenvalues of the Laplacian of M. Every smooth function f on M can be written as a sum of eigenfunction.

Suppose Σis a submanifold of M, and Γa submanifold of N. (i). Show that the restriction of χto Σis a smooth map from Σto N. (ii). If the χ(M) ⊂ Γ, show that χis a smooth map from Mto Γ. Example 3.2.1 The groups SL(n,R) and O(n). Each of these groups is con-tained as a submanifold in GL(n,R). This implies that SL(n,R)×SL(n,R) and O(n) × O(n) are submanifolds of GL(n,R) × GL(n,R. ** мат**. погружённое многообрази But Did You Check eBay? Find Immersed On eBay. Check Out Immersed On eBay. Find It On eBay

- -imal. For proving Theorem 1.1, the.
- Register the immersion of the immersed submanifold. A topological immersion is a continuous map that is locally a topological embedding (i.e. a homeomorphism onto its image). A differentiable immersion is a differentiable map whose differential is injective at each point. If an inverse of the immersion onto its image exists, it can be registered at the same time. If the immersion depends on.
- IMMERSED IN A COMPLEX SPACE FORM TAKEHJRO ITOH Dedicated to Professor T. Otsuki on his 60th birthday Abstract. The author gives the partial solution for the conjecture; a Kaehler submanifold in a complex space form of constant holomorphic sectional curvature 1 is totally geodesic if ever its holomorphic sectional curvature is greater than i
- By an immersed submanifold of Euclidean space RN I will mean a diﬀeren-tiable manifold Mtogether with an immersion X: M → RN. Note that for any x∈ Mthere is a neighbourhood Uof xsuch that X| U is an embedding. A particular case of an immersed submanifold is an embedded submanifold. The inner product ˇ.,.ˆ on RN induces a metric gand corresponding Levi-Civita connection ∇ on M.

Kaehler submanifold immersed in M (i.e., complex submanifold with the induced Kaehler structure). Let J (resp. J) be the complex structure of M (resp. M) and g (resp. g) be the Kaehler metric of M (resp. M). We denote by V (resp. V) the covariant differentiation with respect to g (resp. g). Then the second fundamental form a of the immersion is. So the immersed submanifold ##N## certainly is a manifold in its own sense, but ##i## might not be an embedding, thus the topology of ##N## and the subspace topology of ##i(N)## might have nothing to do with eachother. I don't think you should see an immersed submanifold as a subset of the manifold. A better way to see it is as a manifold such that an immersion to the big manifold exists. This. ** Increasing union of embedded submanifold is immersed manifold**. Ask Question Asked 1 year, 9 months ago. Active 1 year, 4 months ago. Viewed 186 times 1 $\begingroup$ While working on the proof of the stable manifold theorem, I came across a problem that I'm not able to really grasp. Given some.

** immersed submanifold in a unique way**. \Immersion is undoubtedly an important notion. But I person-ally am not aware of a usage of the general notion of \immersed sub-manifold beyond that of the notion of an \immersion, especially in situations like the gure eight. On the other hand, there is another notion { a \di eological sub- manifold { that I nd useful. A di eological submanifold of M. The top diagram is incorrect - an immersed submanifold is the image of an injective immersion, and hence cannot have self-intersections. --18.87.1.187 19:23, 11 September 2007 It's true that the image is in conflict with the definition given. In my experience, people often use the words immersed submanifold to refer to submanifolds with self-intersections, so I vote for changing the.

compact Kaehler submanifold immersed in Pm{C). Itis natural to conjecture the following: If theholomorphic sectionalcurvature of M =^1/2,then M is a totallygeodesic Pn{C),a Veronese Pn(C),a Segre submanifold Pk(C)xPn-k(C) or a Hermitian sym-metric space of rank 2 with parallelsecond fundamental form. To prove thisconjecture,in view of Theorem 7.4in [3]itis sufficientto show that the second. In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. In the following we assume all manifolds are differentiable manifolds of. In this note we consider the Liouville type theorem for a properly immersed submanifold M in a complete Riemmanian manifold N. Assume that the sectional curvature \(K^N\) of N satisfies \(K^N\ge -L(1+dist_N(\cdot ,q_0)^2)^\frac{\alpha }{2}\) for some \(L>0, 2>\alpha \ge 0\) and \(q_0\in N\)

- When a Legendrian submanifold admits a generating family (GF), Sablo and Traynor proved that there is an isomorphism between the GF-cohomology groups of the Leg-endrian and the cohomology groups of any GF-compatible embedded Lagrangian lling. In this paper, we show that a similar isomorphism exists for immersed GF
- Let be an isometrically immersed submanifold of (LCS)-manifold . Then, is invariant submanifold if and only if the normal space , at every point , admits an orthonormal basis consisting of the eigenvectors of the matrix . Proof. Let us suppose that is invariant. (1) When is normal to , at we consider an -dimensional vector space and investigate the eigenvalues of the matrix . From and , it is.
- read. In this lecture we prove the manifold version of the Implicit Function Theorem. Along.
- A submanifold is a manifold inside another manifold. Definition. For a homomorphism of differentiable manifolds. X ↪ Y X \hookrightarrow Y to qualify as a submanifold inclusion it is usually required to be an embedding of differentiable manifolds, hence. an embedding of topological spaces; an immersion of differentiable manifolds. References. See also. Wikipedia, Submanifold; Last revised on.
- Let (M,g) be a Riemannian manifold and consider a immersed submanifold ι : N → M. This means that N is a smooth manifold and ι is an injective immersion. Then the Riemannian metric g induces a Riemannian metric gN in N as follows. Let p ∈ N. The tangent space TpN can be viewed as a subspace of TpM via the injective map dιp: TpN → Tι(p)M. We deﬁne (gN)p to be simply the restriction.
- Submanifold: | | ||| | Immersed manifold straight line with selfintersections... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled
- Submanifolds of differentiable manifolds¶. Given two differentiable manifolds \(N\) and \(M\), an immersion \(\phi\) is a differentiable map \(N\to M\) whose differential is everywhere injective. One then says that \(N\) is an immersed submanifold of \(M\), via \(\phi\).. If in addition, \(\phi\) is a differentiable embedding (i.e. \(\phi\) is an immersion that is a homeomorphism onto its.

submanifold Km ˆS2m+1, what combinations ofBetti numbersand double pointscan be realized by a smooth ﬁlling Fm+1 ˆB2m+2? 9restrictions from algebraic topology for embedded ﬁllings I would like to know if others know anything about this problem! Lisa Traynor (Bryn Mawr) Geography of Immersed Lagrangian Fillings Symplectic Zoominar 8/51. Higher-Dimensional Geography Smooth Geography. Submanifold A (infinitely differentiable) manifold is said to be a submanifold of a manifold if is a subset of and the identity map of into is an embedding . SEE ALSO: Embedding , Manifold , Subfield , Subspac As a corollary, we give that any biharmonic properly immersed submanifold in a hyperbolic space is minimal. These results give affirmative partial answers to the global version of generalized Chen's conjecture

Submanifold. From Wikipedia, the free encyclopedia. Immersed manifold straight line with self-intersections. In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors. Let be an immersed submanifold of an almost para-Hermitian manifold and a differentiable distribution on . We denote the orthogonal distribution to on by . Then, for all , we write where and are orthogonal projections on and , respectively. Next, we will give a sufficient and necessary condition for a distribution to be slant. Theorem 7. Let be a submanifold of an almost para-Hermitian. We prove that a compact, immersed, submanifold of C^n, lagrangian for a Kahler form, is rationally convex, generalizing a theorem of Duval and Sibony for embedded submanifolds Note that if X is a compact submanifold of X, then f(X) is in fact a compact smooth submanifold of N (since fj X: X !N is an embedding), and f is a di eo-morphism from Xonto f(X). In the example above, the bad thing is that the image f(X) of Xis not a smooth submanifold of T2 (but only an immersed submanifold) angles, a compact submanifold M of real dimension 2n, immersed into a Ka¨hler-Einstein mani-fold N of complex dimension 2n, must be either a complex or a Lagrangian submanifold of N, or have constant Ka¨hler angle, depending on n = 1, n = 2, or n ≥ 3, and the sign of the scalar curvature of N. These results generalize to non-minimal submanifolds some known results for minimal submanifolds.

de nition called an immersed submanifold. (a) Show that S Mis a k-dim submanifold if and only if 8p2S, there exists a C1 map F: U!Rn k on a neighbourhood Uof pin Msuch that 0 is a regular value and U\S= F 1(0). Remark: This shows that submanifolds are locally the level set of a function and gives a third equivalent de nition of a submanifold. (b) Show that S Mis a submanifold if and only if. In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S rarr; M satisfies certain properties. There are different types of submanifolds depending on exactly whic The submanifold R is said to be properly immersed if, for any compact subset X in M, the pre-image i 1ðXÞ is compact in R. A function on a Riemannian manifold is called proper if for any compact set in R, its pre-image is compact. 3 Equivalence of properness of immersion, finiteness of weighted volume and polynomial volume growth In Riemannian geometry, the classical Bishop volume comparison. 2n+1)-dimensional algebra anti-invariant submanifold called codimension complex manifold complex projective space complex space form complex structure components constant curvature constant holomorphic sectional contact manifold contact structure coordinate system covariant CR submanifold curvature tensor curvature vector defined denote Differential Geometry dimension equation f-structure flat.

- imal. These results give affirmative partial answers to the global version of generalized Chen's conjecture.Comment: 11 pag
- compact Kaehler submanifold immersed in Pm(C). It is natural to conjecture the following : If the holomorphic sectional curvature of M i^l/2, then M is a totally geodesic Pn(C)t a Veronese Pn(C), a Segre submanifold Pk(C)xPn-k(C) or a Hermitian sym~ metrìc space of rank 2 with parallel second fundamental form . To prove this conjecture, in view of Theorem 7.4 in [3] it is sufficient to show.
- ing the subtle relationship between submanifold and ambient CR density bundles the authors are able to invariantly relate these two tractor bundles, and hence to invariantly relate the normal Cartan connections of the submanifold and ambient manifold by a tractor analogue of the Gauss formula. This also leads to CR analogues of the Gauss, Codazzi, and Ricci equations. The tractor.

Rational convexity of non-generic immersed Lagrangian submanifolds 29 remains Lagrangian for the new form ddcφ, and this form coincides with ω outside a neighborhood of 0. Adding a similar term for L2 concludes. References 1. Auroux, D., Gayet, D., Mohsen, J.-P.: Symplectic hypersurfaces in the complement of an isotropic submanifold. Math submanifold immersed in a complex projective space to be totally geodesic is given in terms of sectional curvature. 1. Statement of result. Let P(C) be an «-dimensional complex projective space with the Fubini-Study metric of constant holomorphic sectional curva-ture c, and let M be an «-dimensional complete totally real minimal subman- ifold immersed in Pn(C). The purpose of this paper. Complete linear Weingarten hypersurfaces immersed in the hyperbolic space DE LIMA, Henrique Fernandes, Journal of the Mathematical Society of Japan, 2014; On hypersurfaces into Riemannian spaces of constant sectional curvature Caminha, Antonio, Kodai Mathematical Journal, 2006; On submanifolds with parallel mean curvature vector Araújo, Kellcio O. and Tenenblat, Keti, Kodai Mathematical. I will describe the area functional for immersed sub-manifolds in a sub-Riemannian structure. Since we are interested in high codimensional submanifolds, the notion of degree introduced by Magnani and Vittone is a central tool in this setting. We will see that the area functional depends on the degree of the immersed submanifold. Then, it turns out that not all the possible variations are.

0 be a regularly immersed submanifold with immersion ϕ: Mm → Σ 0 ⊂ N. We make use of the induced metric ˚g= ϕ∗hon M. The Levi-Civita-connection compatible with˚gis denoted by ˚∇. The connection on the pull-back bundle ϕ∗TNis denoted by ∇b, and members of ϕ∗TNare called vector ﬁelds along ϕ. Using this notation we introduce the second fundamental form of ϕdeﬁned as. **submanifold** definition: Noun (plural **submanifolds**) 1. (topology) A manifold which is a subset of another, so that the inclusion function is an embedding or, sometimes, an immersion.. On minimal generic submanifolds immersed in S 2 m + 1. Masahiro Kon. Colloquium Mathematicae (2001) Volume: 90, Issue: 2, page 299-304; ISSN: 0010-1354; Access Full Article top Access to full text Full (PDF) Abstract top We give a pinching theorem for a compact minimal generic submanifold with flat normal connection immersed in an odd-dimensional sphere with standard Sasakian structure. How to.

Let i : N ,→ M be a connected submanifold that is an integral curve for L, 3 so N is 1-dimensional. We assume i(N) meets N m 0 and we seek to prove that i factors (necessarily uniquely) through a C∞ map from N to N m 0. The preimage i−1(N m 0) is closed and non-empty in the connected manifold N, so to prove it equals N it suﬃces to prove openness. This is a local problem near each. We prove that an immersed lagrangian submanifold in $\C^n$ with quadratic self-tangencies is rationally convex. This generalizes former results for the embedded and the immersed transversal cases Saatchi Art is pleased to offer the drawing, The Immersed Submanifold, by James Roper. Original Drawing: Pencil on Paper. Size is 0 H x 0 W x 0 in If $ Y $ is an immersed submanifold, then $ {\mathcal N} _ {Y/X} $ and $ {\mathcal N} _ {Y/X} ^ {*} $ are called the normal and conormal sheaves of the submanifold $ Y $. 2) $ ( X, {\mathcal O} _ {X} ) $ is an irreducible separable scheme of finite type over an algebraically closed field $ k $, $ ( Y, {\mathcal O} _ {Y} ) $ is a closed subscheme of it and $ f: Y \rightarrow X $ is an imbedding. 2020-08-04T04:54:19Z https://tsukuba.repo.nii.ac.jp/?action=repository_oaipmh oai:tsukuba.repo.nii.ac.jp:00015818 2020-07-21T06:43:18Z 00003:00062:05602:00091:0289

Formal Definition - Immersed SubmanifoldsAn immersed manifold of a manifold M is the image S of an immersion map f N → M in general this image will not be a submanifold as a subset, and an immersion map need not even N → M be an inclusion (one-to-one), in which we call it an injective immersion, and define an immersed submanifold to be the image subset S f N → M the image of N in. As nouns the difference between immersion and submanifold is that immersion is the act of immersing or the condition of being immersed while submanifold is (topology) a manifold which is a subset of another, so that the inclusion function is an embedding or, sometimes, an immersion gt.geometric topology - What is an immersed submanifold? Bing's house with two rooms is the image of an immersed sphere that is not in general position. General position immersions are easy to build out of local pictures --- well sort of easy to build More generally, for an immersed submanifold F: Mn! Pm, we deﬂne the pulled-back metric gM (V;W) + hF ⁄V;F⁄Wi (12) for V;W 2 TpM. For convenience, later we shall often drop the subscript M for g. In the following we assume that F: M ! P is an immersed submanifold. Let ¡ U; ' xi n i=1 ¢ be a local coordinate system on M and assume that F restricted to U is an embedding. Then ' @F @xi.

We prove that a compact, immersed, submanifold of C^n, lagrangian for a Kahler form, is rationally convex, generalizing a theorem of Duval and Sibony for.. We will use the term immersed submanifold. De nition. Suppose N and M are manifolds and f : N ! M is an immersion. Then (N;f) is an immersed submanifold. This terminology is suggested by Exercise 1.*** Proposition 6.5***. Suppose Nand Mare manifolds and f: N! Mis a one-to-one immersion. If Nis compact, then fis an embedding. Proof. We just need to show that fis a homeomorphism to its image. It. Now, let M be an isometrically immersed submanifold in M¯ . In the rest of this paper, we assume the submanifold M of M¯ is tangent to the structure vector ﬁeld ξ. Then the formulas of Gauss and Weingarten for M in M¯ are given, respectively, by ∇¯ XY =∇XY +h(X,Y) (4) 184 M. Atc.eken, S. D´ır´ık and ∇¯ XV =−AVX+∇⊥V (5) for any X,Y ∈ Γ(TM)and V ∈ Γ(T⊥M), where.

- Here is classic example of an immersed submanifold that is not homeomorphic to its image in the subspace topology. Think of a torus as the quotient of the Eulicdean plane obtained by identifying points whose ##(x,y)## coordinates differ by an integer. A straight line that makes an irrational angle with the ##x##-axis projects to an immersed 1 dimensional submanifold. The image of the line is. immersed submanifold nedir ve immersed submanifold ne demek sorularına hızlı cevap veren sözlük sayfası. (immersed submanifold anlamı, immersed submanifold Türkçesi, immersed submanifold nnd xM, Derivatives) Suppose that Mis a smooth m-dimensional submanifold of some Euclidean space RN. (We will see in Theorem 18 that every manifold can be realized this way). Let ˚: U! Mbe a local parameterization around some point x2Mwith ˚(0) = x. We deﬁne the tangent space T xMto be the image of the map d˚ 0: Rm!RN. Note that T xMis an m-dimensional subspace of RN; its translate x+T xM is. An immersed submanifold of a manifold M is the image S of an immersion map f: N → M; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) - it can have self-intersections.. More narrowly, one can require that the map f: N → M be an injection (one-to-one), in which we call it an injective immersion, and define an : 2. Immersed submanifold: Wikipedia, the Free Encyclopedia [home, info] Words similar to immersed submanifold Usage examples for immersed submanifold Words that often appear near immersed submanifold Rhymes of immersed submanifold Invented words related to immersed submanifold: Search for immersed submanifold on Google or Wikipedia. Search completed in 0.045 seconds. Home Reverse Dictionary.

Immersed submanifolds as representatives of singular homology classes --The transverse class to an immersed submanifold --Homology of multiple points of immersed manifolds. Series Title: Memoirs of the American Mathematical Society, no. 250. Responsibility: by Ralph J. Herbert submanifold immersed in an almost paracontact Riemannian manifold to be invariant and show further properties of invariant submanifold in a manifold with the (';»;·;G)-structure. 1. (';»;·;G)-structure Let M be an m-dimensional diﬁerentiable manifold. If there exist on M a (1;1)-tensor ﬂeld ', a vector ﬂeld » and a 1-form · satisfying ·(») = 1; '2 = I ¡· ›»; (1. English: Image of an injectively immersed submanifold that is not an embedding. Date: 25 September 2017: Source: Inkscape: Author: Bobbrick: Licensing . Public domain Public domain false false: I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this. Workshop on Submanifold Theory and Geometric Analysis UFSCar, São Carlos, Brazil, August 05 09, 2019 Wednesday- 11:30 h - 12 h -Auditório do DM Adriano Cavalcante Bezerra (IFG - Brazil) Rigidity of Submanifolds in a Constant Curvature Space Abstract. Let M be a complete submanifold with constant mean curaturev immersed in According to the paper by Hass and Hughes [6], an orientable 2-manifold of genus g, immersed in Euclidean 3D space (R3), has 4g regular homotopy classes. Surfaces belong to the same class if they can be smoothly transformed into one another without ever experiencing any cuts, or tears, or creases with infinitely sharp curvature; however, the surface is allowed to pass through itself. For genus.