de Sitter空间中具有平行平均曲率向量的完备类空子流形

Complete Space-like Submanifolds in a de Sitter Space with Parallel Mean Curvature

证明了deSitter空间中具有平行平均曲率向量的完备类空子流形 ,当第二基本形式的模长平方S <2 n - 1c时 。

Let M be a complete n dimensional  space like submanifold in the de sitter space S n+p p(c) with parallel mean curvature vector. Denote by S the squared length of the second fundamental form of M . In the present paper it is shown that if S<2n-1c , then M is totally unbilical.