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Horo-tight spheres in Hyperbolic space
| Title: | Horo-tight spheres in Hyperbolic space |
| Authors: | Buosi, Marcelo Browse this author | | Izumiya, Shyuichi Browse this author | | Maria Aparecida, Soares Ruas Browse this author |
| Issue Date: | 14-Jan-2009 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 932 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by T. Cecil and P. Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69740 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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