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Geometry of 1-lightlike submanifolds in anti-de Sitter n-space

Published online by Cambridge University Press:  25 September 2013

Zhigang Wang ,
Donghe Pei  and
Liang Chen
Zhigang Wang
Affiliation:
School of Mathematics Science, Harbin Normal University, Harbin 150500, People's Republic of China and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People's Republic of China, ([email protected])
Donghe Pei
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People's Republic of China, ([email protected]; [email protected])
Liang Chen
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, People's Republic of China, ([email protected]; [email protected])
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Abstract

In this paper we investigate the differential geometry of 1-lightlike submanifolds in anti-de Sitter n-space as an application of the theory of Legendrian singularities. Based on some theory of lightlike submanifolds, we also introduce the notion of 1-lightlike horospherical Gauss curvature, which is important for us to study the singularities of 1-lightlike horospherical hypersurfaces. Moreover, we discuss the related geometric property of 1-lightlike horospherical hypersurfaces in anti-de Sitter n-space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 5 , October 2013 , pp. 1089 - 1113
Copyright
Copyright © Royal Society of Edinburgh 2013 

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