Shen's L-Process on the Chern Connection‎

Document Type : Original Article

Authors

1 Department of Pure Mathematics. Faculty of Mathematical Sciences. University of Tabriz. Tabriz. Iran.

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

Abstract

‎The notion of Shen's process was introduced by Tayebi-Najafi in order to construct the Shen connection from the Berwald connection‎. ‎In this paper‎, ‎we study the connection obtained by Shen's L-process on the Chern connection‎. ‎Let (M‎, ‎F) be a Finsler manifold‎. ‎Suppose that D is the linear torsion-free connection obtained by Shen's L-process on Chern's connection‎. ‎First‎, ‎we show the existence and uniqueness of D‎. ‎Then‎, ‎we prove that their hv-curvature coincides if and only if F is a Riemannian ‎metric

Keywords

Journal of Finsler Geometry and its Applications
Volume 4, Issue 1
July 2023
Pages 12-22

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