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Abstract
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In this paper, we study the Landsberg curvature of a Finsler metric via
conformal navigation problem. We show that the Landsberg curvature of
is proportional to its
Cartan torsion where
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
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.
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Keywords
Finsler metric, Landsberg curvature, conformal navigation
problem
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Mathematical Subject Classification 2010
Primary: 53B40, 58E20
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Milestones
Received: 9 February 2017
Revised: 30 June 2018
Accepted: 4 January 2019
Published: 5 November 2019
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