Shen's L-Process on the Chern Connection‎

‎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:

Chern connection‎ , ‎Shen connection‎ , ‎Shen's C and L-Processes