On the Landsberg curvature of a class of Finsler metrics generated from the navigation problem

Libing Huang, Huaifu Liu and Xiaohuan Mo

Vol. 302 (2019), No. 1, 77–96

DOI: 10.2140/pjm.2019.302.77

Abstract

In this paper, we study the Landsberg curvature of a Finsler metric via conformal navigation problem. We show that the Landsberg curvature of $F$ is proportional to its Cartan torsion where $F$ is the Finsler metric produced from a Landsberg metric and its closed vector field in terms of the conformal navigation problem generalizing results previously known in the cases when $F$ is a Randers metric or the Funk metric on a strongly convex domain. We also prove that the Killing navigation problem has the Landsberg curvature preserving property for a closed vector field.

Keywords

Finsler metric, Landsberg curvature, conformal navigation problem

Mathematical Subject Classification 2010

Primary: 53B40, 58E20

Milestones

Received: 9 February 2017

Revised: 30 June 2018

Accepted: 4 January 2019

Published: 5 November 2019