局部对称的伪黎曼流形中的极大类空子流形

Maximal space like submanifolds in locally symmetric pseudo Riemannian spaces.

:Nn+ pp 为 n+ p维局部对称的完备连通伪黎曼流形 ,它的截面曲率 KN 满足 c1 ≤ KN≤ c2 .Mn为 Nn+ pp 中的极大类空子流形 .给出了 Mn 完备或紧致情况下它的第二基本形式模长平方的估计 .

Let N n+p p be a locally symmetric, complete and connected pseudo Riemannian manifold, whose sectional curvature K N satisties c 1≤K N≤c 2. Let M n be a maximal spaclike submanifold in N n+p p . An estimate is given for the square of the length of the second fundamental form of M n when M n is complete or compact, and the results obtained by Ishihara and W. D. Song respectively are generalized.