Linear Weingarten spacelike submanifolds in de Sitter space

摘要

Let M n be a spacelike linear Weingarten submanifold in a de Sitter space ${S^{n+p}_{p}(1)}$ with R = aH + b, where R and H are the normalized scalar curvature and the length of the mean curvature vector respectively. In this paper, we give intrinsic and extrinsic conditions for M n to be totally umbilical, respectively.