Tripathi Connection in Finsler Geometry

Abstract

Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated. Such connection unifies all formerly known Finsler connections and some other connections not been introduced so far. Also, our connection is a Finslerian version of the Tripathi connection introduced in Riemannian geometry. The existence and uniqueness of such connection are proved intrinsically. An explicit intrinsic expression relating this connection to Cartan connection is obtained. Some generalized Finsler connections are constructed from the Tripathi Finsler connection, by applying the ${P}^{1}$-process and ${C}$-process introduced by Matsumoto. Finally, under certain conditions, many special Finsler connections are given.