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Complete maximal spacelike surfaces in ananti-de Sitter space {\bf H}^{4}_{2}(c)

Published online by Cambridge University Press:  07 August 2001

Qing-Ming Cheng
Qing-Ming Cheng
Affiliation:
Department of Mathematics, Faculty of Science, Josai University, Sakado, Saitama 350-0295, Japan. Email:cheng@math.josai.ac.jp
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Abstract

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In this paper, we prove that if M^2 is a complete maximal spacelike surface of an anti-de Sitter space {\bf H}^{4}_{2}(c) with constant scalar curvature, then S=0, S={-10c\over 11}, S={-4c\over 3} or S=-2c, where S is the squared norm of the second fundamental form of M^{2}. Also

(1) S=0 if and only if M^2 is the totally geodesic surface {\bf H}^2(c);

(2) S={-4c\over 3} if and only if M^2 is the hyperbolic Veronese surface;

(3) S=-2c if and only if M^2 is the hyperbolic cylinder of the totally geodesic

surface {\bf H}^{3}_{1}(c) of {\bf H}^{4}_{2}(c).

1991 Mathematics Subject Classifaction 53C40, 53C42.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 139 - 156
Copyright
2000 Glasgow Mathematical Journal Trust

Footnotes

Research partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture and by a Grant-in-Aid for Scientific Research from Josai University.