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.

arXiv comment16 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

References in corpus (5)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• On the interplay between Lorentzian Causality and Finsler metrics of Randers type
• Open problems and questions about geodesics
• Chains in CR geometry as geodesics of a Kropina metric
• Geodesics on strong Kropina manifolds

Cited by in corpus (6)

• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• A note on the Sagnac effect in general relativity as a Finslerian effect
• An account on links between Finsler and Lorentz Geometries for Riemannian Geometers
• On closed geodesics in Lorentz manifolds
• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
• On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology