Abstract
AbstractWe study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature ofM, 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.
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