# Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Czechoslovak Mathematical Journal (2007)

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

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topWang, 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 -

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