Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2001; 38(1): 135-146

Printed January 1, 2001

Copyright © The Korean Mathematical Society.

Space-like submanifolds with constant scalar curvature in the de Sitter spaces

Liu Ximin

Dalian University of Technology

Abstract

Let $M^n$ be a space-like submanifold in a de Sitter space $M_p^{n+p}(c)$ with constant scalar curvature. We firstly extend Cheng-Yau's technique to higher codimensional cases. Then we study the rigidity problem for $M^n$ with parallel normalized mean curvature vector field.

Keywords: space-like submanifold, scalar curvature, normalized mean curvature vector field

MSC numbers: 53C40, 53C42, 53C50