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.

中文翻译：

---

沉关于 Berwald 连接的 L 过程

使用其他众所周知的连接的松本工艺无法获得沉连接。因此，Tayebi 和 Najafi 引入了两个新过程，称为沉 C 过程和 L 过程，并表明沉连接是通过沉 C 过程从陈连接获得的。我们研究了 Berwald 连接上的 Shen 的 C - 和 L - 过程，并在 Finsler 几何中引入了两种新的无扭连接。然后我们获得这些连接的所有黎曼和非黎曼曲率。通过使用这个结果，我们找到了这些连接的 hv -curvatures 的显式形式，并证明这些 hv -curvatures 当且仅当 Finsler 结构简化为 Berwaldian 或 Riemannian 结构时才消失。作为一个应用，我们考虑紧凑的 Finsler 流形并获得 ODE。