Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space

被引：1
|
作者：
Kobayashi, Honoka [1 ]
Koike, Naoyuki [1 ]
机构：
[1] Tokyo Univ Sci, Fac Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan
来源：
MATHEMATISCHE NACHRICHTEN | 2020年 / 293卷 / 05期
关键词：
anti-de Sitter space; B-scroll; complex circle; finite type; pseudo-hyperbolic Gauss map; SPHERICAL SUBMANIFOLDS; CLASSIFICATION;
D O I：
10.1002/mana.201800447
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non-diagonalizable shape operator in the 3-dimensional anti-de Sitter space. Also, we investigate the behavior of type numbers of the pseudo-hyperbolic Gauss map along the parallel family of such oriented Lorentzian surfaces in the 3-dimensional anti-de Sitter space. Furthermore, we investigate the type number of the pseudo-hyperbolic Gauss map of one of Lorentzian hypersurfaces of B-scroll type in a general dimensional anti-de Sitter space.
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页码：923 / 944
页数：22
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