Wadsley's Theorem in pseudo-Riemannian Geometry

Details Wadsley's Theorem in pseudo-Riemannian Geometry Wadsley's Theorem in pseudo-Riemannian Geometry

2011-11-25

arxiv.org/abs/1111.5975v2

Mathematics

Differential Geometry

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

Scientific paper

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 $S^1\times \R$. Further we show that every pseudo-Riemannian
2-manifold with index 1 contains a non-closed timelike or spacelike geodesic.

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