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Space-like submanifolds with parallel mean curvature in de Sitter spaces

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Chongzhen Ouyang  and
Zhenqi Li
Zhenqi Li
Affiliation:
Department of Mathematics Nanchang University Nachang330047 P. R. of China e-mail: [email protected]
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Abstract

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This paper investigates complete space-like submainfold with parallel mean curvature vector in the de Sitter space. Some pinching theorems on square of the norm of the second fundamental form are given

Keywords

de Sitter spacespace-like submanifoldmean curvature vectorparallel

MSC classification

Secondary: 53C40: Global submanifolds 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 1 - 7
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Akutagawa, K., ‘On space-like hypersurfaces with constant mean curvature in the de Sitter space’, Math. Z. 196 (1987), 13–19.CrossRefGoogle Scholar
[2]Cheng, Q., ‘Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector’, Math. Z. 206 (1991), 333–339.CrossRefGoogle Scholar
[3]Goddard, A. J., ‘Some remarks on the existence of spacelike hypersurfaces of constant mean curvature’, Math. Proc. Cambridge Philos. Soc. 82 (1977), 489–495.CrossRefGoogle Scholar
[4]Omori, H., ‘Isometric immersions of Riemannian manifolds’ J. Math. Soc. Japan 19 (1967), 205–214.Google Scholar
[5]Ouyang, C. and Li, Z., ‘Complete space-like hypersurfaces with constant mean curvature in the de Sitter spaces’, Chinese Quart. J. Math., to appear.Google Scholar
[6]Ramanathan, J., ‘Complete spacelike hypersurfaces of constant mean curvature in a de Sitter space’, Indiana Univ. Math. J. 36 (1987), 349–359.CrossRefGoogle Scholar
[7]Santos, W., ‘Submanifolds with parallel mean curvature in spheres’, Tôhoku Math. J. 46 (1994), 405–415.CrossRefGoogle Scholar
[8]Yau, S. T., ‘Submanifolds with constant mean curvature I’, Amer. J. Math. 96 (1974), 346–366.CrossRefGoogle Scholar
[9]Yau, S. T., ‘Harmonic functions on complete Riemannian manifolds’, Comm. Pure Appl. Math.. 28 (1975), 201–228.CrossRefGoogle Scholar