Wadsley's Theorem in pseudo-Riemannian Geometry

Stefan Suhr

Wadsley's Theorem in pseudo-Riemannian Geometry

Differential Geometry 2012-02-20 v2 Dynamical Systems

Authors: Stefan Suhr

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.

Keywords

geodesics and riemannian geometry riemannian geometry foliations

Cite

@article{arxiv.1111.5975,
  title  = {Wadsley's Theorem in pseudo-Riemannian Geometry},
  author = {Stefan Suhr},
  journal= {arXiv preprint arXiv:1111.5975},
  year   = {2012}
}

Comments

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

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