Horospherical flat surfaces in Hyperbolic 3-space
-
- Izumiya Shyuichi
- Department of Mathematics, Hokkaido University
-
- Saji Kentaro
- Department of Mathematics, Faculty of Education, Gifu University
-
- Takahashi Masatomo
- Mathematical Science, Muroran Institute of Technology
Search this article
Abstract
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.
Journal
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 62 (3), 789-849, 2010
The Mathematical Society of Japan
- Tweet
Details 詳細情報について
-
- CRID
- 1390001205115419520
-
- NII Article ID
- 10027870826
-
- NII Book ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- NDL BIB ID
- 10764087
-
- Text Lang
- en
-
- Data Source
-
- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
-
- Abstract License Flag
- Disallowed