Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Closed geodesics in Lorentzian surfaces

Author: Stefan Suhr
Journal: Trans. Amer. Math. Soc. 365 (2013), 1469-1486
MSC (2010): Primary 53C22, 53C50
Published electronically: July 11, 2012
MathSciNet review: 3003271
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Abstract: We show that every closed Lorentzian surface contains at least two closed geodesics. Explicit examples show the optimality of this claim. Refining this result we relate the least number of closed geodesics to the causal structure of the surface and the homotopy type of the Lorentzian metric.

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Stefan Suhr
Affiliation: Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

Keywords: Closed geodesics, Lorentzian manifolds
Received by editor(s): November 22, 2010
Received by editor(s) in revised form: June 27, 2011
Published electronically: July 11, 2012
Article copyright: © Copyright 2012 American Mathematical Society