Horospherical flat surfaces in Hyperbolic 3-space

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概要

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• 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.

• 社団法人 日本数学会の論文
• 2010-07-01

著者

• Takahashi Masatomo

  Mathematical Science Muroran Institute Of Technology

• IZUMIYA Shyuichi

  Department of Mathematics Hokkaido University

• SAJI Kentaro

  Department of Mathematics Faculty of Education Gifu University

• Izumiya Shyuichi

  Department Of Mathematics Faculty Of Science Hokkaido University

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