Wadsley's Theorem in pseudo-Riemannian Geometry

Abstract

We prove Wadsley's theorem for foliations by closed non-lightlike geodesics. As an application we show that every pseudo-Riemannian and non-Riemannian 2-mainfold, all of whose time- or spacelike geodesics are closed, is diffeomorphic to $S^1\times \mathbb{R}$. Further we show that every pseudo-Riemannian 2-manifold with index 1 contains a non-closed timelike or spacelike geodesic.

Reason for withdrawal: A revised version of the paper is now part of arXiv:1112.5652v2