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- Izumiya Shyuichi
- Department of Mathematics, Hokkaido University
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- Saji Kentaro
- Department of Mathematics, Faculty of Education, Gifu University
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- Takahashi Masatomo
- Mathematical Science, Muroran Institute of Technology
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抄録
Recently we discovered a new geometry on submanifolds in hyperbolic n-space which is called 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 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.
収録刊行物
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 62 (3), 789-849, 2010
一般社団法人 日本数学会
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詳細情報 詳細情報について
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- CRID
- 1390001205115419520
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- NII論文ID
- 10027870826
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 10764087
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
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- CiNii Articles
- KAKEN
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- 使用不可