ON MAXIMAL SUBMANIFOLDS IN PSEUDORIEMANNIAN MANIFOLDS

Let N_v~n be an n-dimensional pseudo-Riemannian manifold with index v, M_μ~m an m(<n)-dimensional pseudo-Riemannian submanifold with index μ (≤v) isometrically immersed into N_v~n. If the mean curvature of M_μ~m in N_v~n vanishes identically, then M_μ~m is called an extremal submanifold. Particularly, an extremal submanifold in N with μ=0 and m=n-v is called a maximal spacelike submanifold.