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- Title
Shen's L-Process on Berwald Connection.
- Authors
Faghfouri, M.; Jazer, N.
- Abstract
The Shen connection cannot be obtained by using Matsumoto's processes from the other well-known connections. Hence, Tayebi and 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. 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 Riemannian and non-Riemannian curvatures of these connections. By using this result, we find the explicit form of hv-curvatures of these connections and prove that these hv-curvatures vanish if and only if the Finsler structures are reduced to Berwaldian or Riemannian structures. As an application, we consider compact Finsler manifolds and obtain ODEs.
- Subjects
CURVATURE; GEOMETRY; TORSION theory (Algebra)
- Publication
Ukrainian Mathematical Journal, 2020, Vol 72, Issue 8, p1314
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-020-01850-6