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# Total absolute horospherical curvature of submanifolds in hyperbolic space

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 Title: Total absolute horospherical curvature of submanifolds in hyperbolic space Authors: Buosi, Marcelo Browse this author Izumiya, Shyuichi Browse this author Soares Ruas, Maria Aparecida Browse this author Keywords: hyperbolic space horospherical geometry the Chern-Lashof type inequality Issue Date: 2007 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 880 Start Page: 1 End Page: 16 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69689 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics