SPACELIKE SUBMANIFOLDS IN THE DE SITTER SPACE S_p^(n+p)(c) WITH CONSTANT SCALAR CURVATURE

Let Mn be a closed spacelike submanifold isometrically immersed in de Sitter space S^n+p _p(c).Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of Mn,respectively.Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for Mn immersed in ~S^n+p _p(c) with parallel normalized mean curvature vector field is proved.When n≥3, the pinching constant is the best.Thus,the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math,1998,95:499-505) is corrected.Moreover,the reduction of the codimension when Mn is a complete submanifold in S^n+p _p(c) with parallel normalized mean curvature vector field is investigated.

Rigidity Theorems of Spacelike Submanifolds in de Sitter Spaces

In this paper,we study the compact spacelike submanifolds in the de Sitter space,under the assumption that the normalized mean curvature vector is parallel in the normal bundle.Using the generalized Cheng-Yau＇s differential operator,we obtain some general rigidity theorems which naturally generalize some existing results.

ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE

In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.