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Horospherical flat surfaces in Hyperbolic 3-space

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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
Horospherical geometry
Horo-flat surfaces
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)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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