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RIGIDITY RESULTS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR IN THE DE SITTER SPACE

Published online by Cambridge University Press:  24 March 2006

A. BRASIL ,
ROSA M. B. CHAVES  and
A. G. COLARES
A. BRASIL
Affiliation:
Departamento de Matemática-UFC, e-mail: [email protected], URL: http://www.mat.ufc.br
ROSA M. B. CHAVES
Affiliation:
Departamento de Matemática-IMEUSP, e-mail: [email protected], URL: http://www.ime.usp.br
A. G. COLARES
Affiliation:
Departamento de Matemática-UFC, e-mail: [email protected], URL: http://www.mat.ufc.br
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Abstract

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In this work we consider a complete spacelike submanifold $M^{n}$ immersed in the De Sitter space $S_{p}^{n+p}(1)$ with parallel mean curvature vector. We use a Simons type inequality to obtain some rigidity results characterizing umbilical submanifolds and hyperbolic cylinders in $S_p^{n+p}(1)$.

Keywords

53C4253A10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 1 , January 2006 , pp. 1 - 10
Copyright
2006 Glasgow Mathematical Journal Trust