English

Connecting and closed geodesics of a Kropina metric

Differential Geometry 2022-08-05 v2 General Relativity and Quantum Cosmology

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.

Keywords

Cite

@article{arxiv.2103.16912,
  title  = {Connecting and closed geodesics of a Kropina metric},
  author = {Erasmo Caponio and Fabio Giannoni and Antonio Masiello and Stefan Suhr},
  journal= {arXiv preprint arXiv:2103.16912},
  year   = {2022}
}

Comments

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