In this paper we prove some results on the number of geodesics connecting two points or two submanifolds on a non-reversible complete Finsler manifold, in particular for complete Randers metrics. We apply the abstract results to the study of light rays and timelike geodesics with fixed energy on a standard stationary Lorentzian manifold.

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.

Finding the fastest path to a desired destination is vitally important task for microorganisms moving in fluid flow. We study this problem by building an analytical formalism overdamped microswimmers on curved manifolds and arbitrary flows. show that solution corresponds geodesics of Randers metric, which asymmetric Finsler metric reflects irreversible character problem. Using example spherical...


 If a non-reversible Finsler norm is the sum of reversible and closed 1-form, then one can uniquely recover 1-form up to potential fields from boundary distance data. We also show rigidity result for Randers metrics where induced by Riemannian metric which rigid. Our theorems generalize results some manifolds. provide an application seismology seismic wave propagates in moving medium.

The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explici...