Shen's $L$-process on Berwald connection

  • M. Faghfouri Univ. Tabriz, Iran)
  • N. Jazer Univ. Tabriz, Iran)
Keywords: Shen’s C and L-Processes, Landsberg metric, Shen connection

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 $C$ and $L$-processes and showed that the Shen connection is obtained from the Chern connection by Shen's $C$-process.  In this paper, we  study the Shen's $C$- and $L$-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 $hv$-curvatures of these connections and prove that $hv$-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.



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Published
18.08.2020
How to Cite
FaghfouriM., and Jazer N. “Shen’s $L$-Process on Berwald Connection”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 8, Aug. 2020, pp. 1134-48, doi:10.37863/umzh.v72i8.6001.
Section
Research articles