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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 8, pp. 1134–1148, August, 2020. Ukrainian DOI: 10.37863/umzh.v72i8.6001.
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Faghfouri, M., Jazer, N. Shen’s L-Process on Berwald Connection. Ukr Math J 72, 1314–1330 (2021). https://doi.org/10.1007/s11253-020-01850-6
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DOI: https://doi.org/10.1007/s11253-020-01850-6