Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2010; 47(5): 1067-1076

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.1067

Copyright © The Korean Mathematical Society.

On complete spacelike $(r-1)$-maximal hypersurfaces in the anti-de Sitter space $\mathbb{H}^{n+1}_1(-1)$

Biaogui Yang

Fujian Normal University

Abstract

In this paper we investigate complete spacelike $(r-1)$-maximal (i.e., $H_r\equiv0$) hypersurfaces with two distinct principal curvatures in the anti-de Sitter space $\mathbb{H}^{n+1}_1(-1)$. We give a characterization of the hyperbolic cylinder.

Keywords: spacelike hypersurface, $(r-1)$-maximal, anti-de Sitter space, hyperbolic cylinder, generalized maximum principle

MSC numbers: 53B30, 53C42, 53C50