Maximal space like submanifolds in locally symmetric pseudo Riemannian spaces.

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.