Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space
Differential Geometry
2018-10-12 v2
Abstract
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 -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 -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.
Keywords
Cite
@article{arxiv.1803.00784,
title = {Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space},
author = {Honoka Kobayashi and Naoyuki Koike},
journal= {arXiv preprint arXiv:1803.00784},
year = {2018}
}
Comments
22pages