Dept. Math, Hokkaido Univ. EPrints Server

Total absolute horospherical curvature of submanifolds in hyperbolic space

Preprint Series # 880
Buosi, Marcelo and Izumiya, Shyuichi and Soares Ruas, Maria Aparecida Total absolute horospherical curvature of submanifolds in hyperbolic space. (2007);

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Abstract

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of $M,$ which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in $3$-space and the horospherical Fenchel and Fary-Milnor's theorems.

Item Type:Preprint
Additional Information:40
Uncontrolled Keywords:hyperbolic space, horospherical geometry, Chern-Lashof type inequality
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:1784