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.

Keywords

• kropina metric
• closed geodesic
• lightlike killing field
• zermelo’s navigation
• 58e10
• 53c22
• 53c60