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Hokkaido University Preprint Series in Mathematics >
Horospherical flat surfaces in Hyperbolic 3-space
| Title: | Horospherical flat surfaces in Hyperbolic 3-space |
| Authors: | Izumiya, Shyuichi Browse this author | | Saji, Kentaro Browse this author | | Takahashi, Masatomo Browse this author |
| Keywords: | Hyperbolic 3-space | | Horosphere | | Horospherical geometry | | Horo-flat surfaces | | Singularities |
| Issue Date: | 20-Mar-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 838 |
| Start Page: | 1 |
| End Page: | 45 |
| Abstract: | Recently we discovered a new geometry on submanifolds in hyperbolic $n$-space which is called {\it horospherical geometry}. Unfortunately this geometry is not invariant under the hyperbolic motions (it is invariant under the canonical action of $SO(n)$), but it has quite interesting features. For example, the flatness in this geometry is a hyperbolic invariant and the total curvatures are topological invariants. In this paper, we investigate the {\it horospherical flat surfaces} (flat surfaces in the sense of horospherical geometry) in hyperbolic $3$-space. Especially, we give a generic classification of singularities of such surfaces. As a consequence, we can say that such a class of surfaces has quite a rich geometric structure. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69647 |
| 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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