Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Qiaoling Wang; Chang Yu Xia

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 435-445
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Wang, Qiaoling, and Xia, Chang Yu. "Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space." Czechoslovak Mathematical Journal 57.1 (2007): 435-445. <http://eudml.org/doc/31140>.

@article{Wang2007,
abstract = {In this paper we study the topological and metric rigidity of hypersurfaces in $\{\mathbb \{H\}\}^\{n+1\}$, the $(n+1)$-dimensional hyperbolic space of sectional curvature $-1$. We find conditions to ensure a complete connected oriented hypersurface in $\{\mathbb \{H\}\}^\{n+1\}$ 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.},
author = {Wang, Qiaoling, Xia, Chang Yu},
journal = {Czechoslovak Mathematical Journal},
keywords = {rigidity; hypersurfaces; topology; hyperbolic space; rigidity; hypersurfaces; topology; hyperbolic space},
language = {eng},
number = {1},
pages = {435-445},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space},
url = {http://eudml.org/doc/31140},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Wang, Qiaoling
AU - Xia, Chang Yu
TI - Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 435
EP - 445
AB - In this paper we study the topological and metric rigidity of hypersurfaces in ${\mathbb {H}}^{n+1}$, the $(n+1)$-dimensional hyperbolic space of sectional curvature $-1$. We find conditions to ensure a complete connected oriented hypersurface in ${\mathbb {H}}^{n+1}$ 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.
LA - eng
KW - rigidity; hypersurfaces; topology; hyperbolic space; rigidity; hypersurfaces; topology; hyperbolic space
UR - http://eudml.org/doc/31140
ER -

References

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