#### Vol. 302, No. 1, 2019

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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
##### 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