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COMPLETE SPACELIKE SUBMANIFOLDS IN DE SITTER SPACES WITH $R= aH+ b$

Part of: Global differential geometry

Published online by Cambridge University Press:  13 February 2013

JIANCHENG LIU  and
JINGJING ZHANG
JIANCHENG LIU*
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, PR China
JINGJING ZHANG
Affiliation:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, PR China email [email protected]
*
✉[email protected]
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Abstract

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In this paper, we give a classification of spacelike submanifolds with parallel normalised mean curvature vector field and linear relation $R= aH+ b$ of the normalised scalar curvature $R$ and the mean curvature $H$ in the de Sitter space ${ S}_{p}^{n+ p} (c)$.

Keywords

de Sitter spacespacelike submanifoldparallel normalised mean curvature vectortotally umbilicalhyperbolic cylinder

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 3 , June 2013 , pp. 386 - 399
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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