Connecting and closed geodesics of a Kropina metric

TL;DR

This paper investigates the existence of connecting and closed geodesics in Kropina metrics, with applications to spacetime null geodesics and navigation problems involving critical wind conditions.

Contribution

It establishes new results on geodesic existence in Kropina metrics, linking geometric properties to physical and navigation applications.

Findings

Existence results for connecting geodesics in Kropina spaces

Existence results for closed geodesics in Kropina spaces

Applications to null geodesics in spacetimes and navigation problems

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.