Total absolute horospherical curvature of submanifolds in hyperbolic space

摘要

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 ChernLashof inequality for surfaces in 3-space and the horospherical Fenchel and FaryMilnor's theorems.