Connecting and closed geodesics of a Kropina metric

Abstract

We prove some results about existence of connecting and closed geodesics in a manifold endowed with a Kropina metric. These have applications to both null geodesics of spacetimes endowed with a null Killing vector field and Zermelo's navigation problem with critical wind.

16 pages, AMSLaTex; v2 matches the published version. A misprint present in the statement of both Th. 5.1 and Cor. 5.2 fixed (they are Th 4.1 and Cor. 4.2 in v1); a correction in the statement of Lemma 3.2 (it is Lemma 2.2 in v1) done; these corrections are not present in the published version

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