de Sitter空间中完备类空子流形的余维数约化

摘要

设Mn为等距浸入到de Sitter空间Spn+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≤n2-√nH2+c,证明了该子流形的余维数p可约化为1.%Let Mn be a complete space-like submanifold isometric immersed into de Sitter space Spn+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 Mn satisfies S≤ n2-√nH2+c,then the codimension p of Mn is reduced to 1.