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.

引用

页码：923 / 944

页数：22

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