Strongly parabolic timelike submanifolds of Minkowsky space

Анотація

R.P. Newman proved that a timelike geodesically complete pseudo-Riemannian manifold with nonnegative Ricci curvature for all vectors and admites a timelike line is isometric to the product of that line and a spacelike complete Riemannian manifold. This result gave a complete proof of a conjecture of Yau. In this paper we proof a cylinder type-theorem which corresponds to the extrinsic version of Newman's result. Moreover, we show that k-strongly parabolic geodesically complete submanifolds of a pseudo-Euclidean space with nonnegative Ricci curvature in the spacelike directions are also cylinders with k-dimensional generators.