Shen s Processes on Finslerian Connections

We discuss the invariant properties of curvatures effected by the Matsumoto’s C or L-process. We find equivalent conditions on curvatures by comparing the difference between the corresponding curvatures of closely related connections. As an application, Matsumoto’s L-process on Randers manifold is studied. Shen’s connection can not be obtained by using Matsumoto’s processes from other connections. This leads us to two new processes which we call Shen’s C and L-processes. We study the invariant properties of curvatures under Shen’s processes