Complete maximal spacelike surfaces in ananti-de Sitter space {\bf H}^{4}_{2}(c)
Glasgow mathematical journal, Tome 42 (2000) no. 1, pp. 139-156
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Inthis paper, we prove that if M^2 is a complete maximalspacelike surface of an anti-de Sitter space {\bfH}^{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 ofM^{2}. Also(1) S=0 if and only if M^2 is the totallygeodesic surface {\bf H}^2(c);(2) S={-4c\over3} if and only if M^2 is the hyperbolic Veronesesurface;(3) S=-2c if and only if M^2 is the hyperboliccylinder of the totally geodesicsurface {\bfH}^{3}_{1}(c) of {\bfH}^{4}_{2}(c).1991 Mathematics Subject Classifaction 53C40, 53C42.
Cheng, Qing-Ming. Complete maximal spacelike surfaces in ananti-de Sitter space {\bf H}^{4}_{2}(c). Glasgow mathematical journal, Tome 42 (2000) no. 1, pp. 139-156. doi: 10.1017/S0017089500010168
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author = {Cheng, Qing-Ming},
title = {Complete maximal spacelike surfaces in ananti-de {Sitter} space {\bf {H}^{4}_{2}(c)}},
journal = {Glasgow mathematical journal},
pages = {139--156},
year = {2000},
volume = {42},
number = {1},
doi = {10.1017/S0017089500010168},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500010168/}
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