Stability of closed characteristics on compact convex hypersurfaces in $\mathbb {R}^6$

Wei Wang

Displaying similar documents to “Stability of closed characteristics on compact convex hypersurfaces in $ℝ^{6}$ ”

On convex hypersurfaces in $E^{n + 1}$

Thomas Hasanis (1984)

Colloquium Mathematicae

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Weingarten hypersurfaces of the spherical type in Euclidean spaces

Cid D. F. Machado, Carlos M. C. Riveros (2020)

Commentationes Mathematicae Universitatis Carolinae

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We generalize a parametrization obtained by A. V. Corro in (2006) in the three-dimensional Euclidean space. Using this parametrization we study a class of oriented hypersurfaces $M^{n}$ , $n \geq 2$ , in Euclidean space satisfying a relation $\sum_{r = 1}^{n} {(- 1)}^{r + 1} r f^{r - 1} (\binom{n}{r}) H_{r} = 0,$ where $H_{r}$ is the $r$ th mean curvature and $f \in C^{\infty} (M^{n}; ℝ)$ , these hypersurfaces are called Weingarten hypersurfaces of the spherical type. This class of hypersurfaces includes the surfaces of the spherical type (Laguerré minimal surfaces). We characterize these hypersurfaces in terms...

Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space $ℂ^{n + 1}$ with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of hypersurfaces with φ or η parallel relative to an induced connection are proved. Also a local characterization of these hypersurfaces is given.

Spacelike intersection curve of three spacelike hypersurfaces in $E_{1}^{4}$

B. Uyar Duldul, M. Caliskan (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space $E_{1}^{4}$ .

On Some Family of Contractible Hypersurfaces in $C^{4}$

S. Kaliman, L. Makar-Limanov (1993)

Cours de l'institut Fourier

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A certain tensor on real hypersurfaces in a nonflat complex space form

Kazuhiro Okumura (2020)

Czechoslovak Mathematical Journal

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In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(φ, ξ, η, g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$ $(= \frac{1}{2} ℒ_{ξ} φ)$ plays an important role in contact Riemannian geometry. In this...

Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product

Antonio W. Cunha, Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima Jr., Adriano A. Medeiros (2016)

Studia Mathematica

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Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product $M ⁿ \times_{ρ} ℝ$ , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related...

Vanishing theorems for Killing vector fields on complete hypersurfaces in the hyperbolic space

Guangyue Huang, Hongjuan Li (2016)

Colloquium Mathematicae

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We study vanishing theorems for Killing vector fields on complete stable hypersurfaces in a hyperbolic space $ℍ^{n + 1} (- 1)$ . We derive vanishing theorems for Killing vector fields with bounded L²-norm in terms of the bottom of the spectrum of the Laplace operator.

Hypersurfaces with singular locus a plane curve and transversal type $A_{1}$

Dirk Siersma (1988)

Banach Center Publications

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Hypersurfaces with constant curvature in $ℝ^{n + 1}$

J. A. Gálvez, A. Martínez (2002)

Banach Center Publications

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We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in $ℝ^{n + 1}$ with constant curvature bounding a planar closed (n-1)-submanifold.

Real hypersurfaces with an induced almost contact structure

Michał Szancer, Zuzanna Szancer (2009)

Colloquium Mathematicae

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We study real affine hypersurfaces $f : M \to ℂ^{n + 1}$ with an almost contact structure (φ,ξ,η) induced by any J-tangent transversal vector field. The main purpose of this paper is to show that if (φ,ξ,η) is metric relative to the second fundamental form then it is Sasakian and moreover f(M) is a piece of a hyperquadric in $ℝ^{2 n + 2}$ .

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Eunmi Pak, Juan de Dios Pérez, Carlos J. G. Machado, Changhwa Woo (2015)

Czechoslovak Mathematical Journal

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We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ and prove non-existence of real hypersurfaces in $G_{2} (ℂ^{m + 2})$ with generalized...

Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

Eunmi Pak, Juan de Dios Pérez, Young Jin Suh (2015)

Czechoslovak Mathematical Journal

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We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ . In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ satisfying such conditions.

Smoothing of real algebraic hypersurfaces by rigid isotopies

Alexander Nabutovsky (1991)

Annales de l'institut Fourier

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Define for a smooth compact hypersurface $M^{n}$ of $R^{n + 1}$ its crumpleness $κ (M^{n})$ as the ratio ${diam}_{R^{n + 1}} (M^{n}) / r (M^{n})$ , where $r (M^{n})$ is the distance from $M^{n}$ to its central set. (In other words, $r (M^{n})$ is the maximal radius of an open non-selfintersecting tube around $M^{n}$ in $R^{n + 1} .)$ We prove that any $n$ -dimensional non-singular compact algebraic hypersurface of degree $d$ is rigidly isotopic to an algebraic hypersurface of degree $d$ and of crumpleness $\leq exp (c (n) d^{α (n) d^{n + 1}})$ . Here $c (n)$ , $α (n)$ depend only on $n$ , and rigid isotopy...

Displaying similar documents to “Stability of closed characteristics on compact convex hypersurfaces in ℝ 6 ”

Displaying similar documents to “Stability of closed characteristics on compact convex hypersurfaces in $ℝ^{6}$ ”