The rigidity theorem for Landsberg hypersurfaces of a Minkowski space

Jin Tang Li

Displaying similar documents to “The rigidity theorem for Landsberg hypersurfaces of a Minkowski space”

Decomposition of $H_{j k h}^{i} (x, \dot{x})$ in generalised recurrent Finsler space of second order

H. D. Pandey, V. J. Dubey (1982)

Matematički Vesnik

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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.

A framed f-structure on the tangent bundle of a Finsler manifold

Esmaeil Peyghan, Chunping Zhong (2012)

Annales Polonici Mathematici

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Let (M,F) be a Finsler manifold, that is, M is a smooth manifold endowed with a Finsler metric F. In this paper, we introduce on the slit tangent bundle $\tilde{T M}$ a Riemannian metric G̃ which is naturally induced by F, and a family of framed f-structures which are parameterized by a real parameter c≠ 0. We prove that (i) the parameterized framed f-structure reduces to an almost contact structure on IM; (ii) the almost contact structure on IM is a Sasakian structure iff (M,F) is of constant flag...

Hypersurfaces with constant $k$ -th mean curvature in a Lorentzian space form

Shichang Shu (2010)

Archivum Mathematicum

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In this paper, we study $n (n \geq 3)$ -dimensional complete connected and oriented space-like hypersurfaces $M^{n}$ in an (n+1)-dimensional Lorentzian space form $M_{1}^{n + 1} (c)$ with non-zero constant $k$ -th $(k < n)$ mean curvature and two distinct principal curvatures $λ$ and $μ$ . We give some characterizations of Riemannian product $H^{m} (c_{1}) \times M^{n - m} (c_{2})$ and show that the Riemannian product $H^{m} (c_{1}) \times M^{n - m} (c_{2})$ is the only complete connected and oriented space-like hypersurface in $M_{1}^{n + 1} (c)$ with constant $k$ -th mean curvature and two distinct principal curvatures, if the multiplicities...

Finsler Space with Rund's H-curvature Tensor Kiljk of a Special Form

B. B. Sinha, B. B. Dwivedi (1983)

Publications de l'Institut Mathématique

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On Certain Conditions Which Reduce a Finsler Space of Scalar Curvature to a Riemannian Space of Constant Curvature

B. B. Sinha, A.S. Matharoo (1986)

Publications de l'Institut Mathématique

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

Thomas Hasanis (1984)

Colloquium Mathematicae

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Hypersurfaces of C2-like Finsler spaces.

Singh, U.P., Gupta, B.N. (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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Complete spacelike hypersurfaces with constant scalar curvature

Schi Chang Shu (2008)

Archivum Mathematicum

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In this paper, we characterize the $n$ -dimensional $(n \geq 3)$ complete spacelike hypersurfaces $M^{n}$ in a de Sitter space $S_{1}^{n + 1}$ with constant scalar curvature and with two distinct principal curvatures one of which is simple.We show that $M^{n}$ is a locus of moving $(n - 1)$ -dimensional submanifold $M_{1}^{n - 1} (s)$ , along $M_{1}^{n - 1} (s)$ the principal curvature $λ$ of multiplicity $n - 1$ is constant and $M_{1}^{n - 1} (s)$ is umbilical in $S_{1}^{n + 1}$ and is contained in an $(n - 1)$ -dimensional sphere $S^{n - 1} (c (s)) = E^{n} (s) \cap S_{1}^{n + 1}$ and is of constant curvature ${(\frac{d {log | λ^{2} - (1 - R) |^{1 / n}}}{d s})}^{2} - λ^{2} + 1$ ,where $s$ is the arc length of an orthogonal trajectory...