Tripathi Connection in Finsler Geometry

TL;DR

This paper introduces a new linear connection in Finsler geometry that unifies existing connections and extends the Tripathi connection from Riemannian geometry, with proofs of existence, uniqueness, and explicit relations to Cartan connection.

Contribution

A novel Finslerian Tripathi connection is proposed, unifying various known Finsler connections and extending the concept from Riemannian geometry.

Findings

Existence and uniqueness of the new connection proved.

Explicit intrinsic relation to Cartan connection established.

Construction of generalized Finsler connections using P1 and C processes.

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 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 is proved intrinsically. An explicit intrinsic expression relating this connection to Cartan connection is obtained. Some generalized Finsler connections are constructed from Tripathi Finsler connection, by applying the P1-process and C-process introduced by Matsumoto. Finally, under certain conditions, many special Finsler connections are given.