Wadsley's Theorem in pseudo-Riemannian Geometry

Stefan Suhr

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arXiv · 1111.5975

Wadsley's Theorem in pseudo-Riemannian Geometry

Stefan Suhr

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

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Stefan Suhr. 2011-11-25. Wadsley's Theorem in pseudo-Riemannian Geometry. https://arxiv.org/abs/1111.5975

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