中文摘要：

设M^n为等距浸入到desitter空间Sp^n＋p（c）中的完备类空子流形，平均曲率H有界且具有平行单位平均曲率向量场．如果M^n的第2基本型模长平方S≤n^2-√n/n H^2＋c/n，证明了该子流形的余维数P可约化为1．

英文摘要：

Let M^n be a complete space-like submanifold isometric immersed into de Sitter space Sp^n＋p （c）, whose mean curvature is bounded with a parallel normalized mean curvature vector field. If the squared norm S of the second fundamental form of M^n satisfies S≤n^2-√n/n H^2＋c/n,then the codimensionp of M^n is reduced to 1.