Closed Geodesics in Lorentzian Surfaces

Details Closed Geodesics in Lorentzian Surfaces Closed Geodesics in Lorentzian Surfaces

2010-11-22

arxiv.org/abs/1011.4878v2

Mathematics

Differential Geometry

Version accepted by the Trans. of the AMS. Section 5 deleted

Scientific paper

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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