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Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Qiaoling Wang, Chang Yu Xia (2007)

Czechoslovak Mathematical Journal

In this paper we study the topological and metric rigidity of hypersurfaces in n + 1 , the ( n + 1 ) -dimensional hyperbolic space of sectional curvature - 1 . We find conditions to ensure a complete connected oriented hypersurface in n + 1 to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.

Totally Umbilical Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

Khan, M. A., Uddin, Siraj, Singh, Khushwant (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C40, 53B25.In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.

Transversally symmetric immersions

José Carmelo González-Dávila, M. C. González-Dávila, Lieven Vanhecke (1997)

Mathematica Bohemica

We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.

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