deSitter空间中完备类空子流形的余维数约化

Reduction of codimension of complete space-like submanifolds in de Sitter spaces

设M^n为等距浸入到de Sitter空间S_p^(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Mn的第2基本型模长平方S满足S≤n^2-n^(1/2)/nH^2+c/n,证明了该子流形的余维数p可约化为1.

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.