Induced and intrinsic Hashiguchi connections on Finsler submanifolds

TL;DR

This paper investigates the geometry of Finsler submanifolds by defining induced and normal connections, and shows conditions under which Hashiguchi connections coincide, advancing understanding of Finsler geometry structures.

Contribution

It introduces a pulled-back approach to Finsler submanifolds and establishes the equivalence of induced and intrinsic Hashiguchi connections under specific conditions.

Findings

Defined the Finsler normal pulled-back bundle.

Derived induced geometric objects like the second fundamental form.

Proved the coincidence of induced and intrinsic Hashiguchi connections under certain conditions.

Abstract

We study the geometry of Finsler submanifolds using the pulled-back approach. We define the Finsler normal pulled-back bundle and obtain the induced geometric objects, namely, induced pullback Finsler connection, normal pullback Finsler connection, second fundamental form and shape operator. Under a certain condition, we prove that induced and intrinsic Hashiguchi connections coincide on the pulled-back bundle of Finsler submanifold.