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
Milestones
Received: 9 February 2017
Revised: 30 June 2018
Accepted: 4 January 2019
Published: 5 November 2019
Authors
Libing Huang
Nankai University
China
Huaifu Liu
Beijing University of Technology
China
Xiaohuan Mo
Peking University
China