On geodesics of Finsler metrics via navigation problem

Huang, Libing; Mo, Xiaohuan

doi:10.1090/S0002-9939-2011-10726-3

On geodesics of Finsler metrics via navigation problem
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by Libing Huang and Xiaohuan Mo PDF

Proc. Amer. Math. Soc. 139 (2011), 3015-3024 Request permission

Abstract:

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 explicitly the geodesics of the Funk metric on a strongly convex domain.

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