On completeness of homogeneous Pseudo-Riemannian manifolds

Marsden, J. E.

Indiana U. Math. J., 22, (1973), 1065-6

Abstract:

The following theorem answers a question raised by J. A. Wolf.

Theorem. Let M be a compact pseudo-riemannian manifold. Let G be a Lie group which acts transitively on M by isometries. Then M is geodesically complete.