Shen's Processes on Finslerian Connections

Details Shen's Processes on Finslerian Connections Shen's Processes on Finslerian Connections

2009-11-18

arxiv.org/abs/0911.3511v1

Mathematics

Differential Geometry

15 pages

Scientific paper

In this paper, 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 connection can not be obtained by using Matsumoto's processes from other well-known 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 the Shen's processes.

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