Abstract
The Shen connection cannot be obtained by using Matsumoto's processes from the other well-known connections. Hence Tayebi–Najafi introduced two new processes called Shen's and -processes and showed that the Shen connection is obtained from the Chern connection by Shen's -process. In this paper, we study the Shen's - and -process on Berwald connection and introduce two new torsion-free connections in Finsler geometry. Then, we obtain all of Riemannian and non-Riemannian curvatures of these connections. Using it, we find the explicit form of -curvatures of these connections and prove that -curvatures of these connections are vanishing if and only if the Finsler structures reduce to Berwaldian or Riemannian structures. As an application, we consider compact Finsler manifolds and obtain ODEs.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
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