About intrinsic Finsler connections for the homogeneous lift to the Osculator Bundle of a Finsler metric

TL;DR

This paper explores the intrinsic Finsler connections on the osculator bundle of a manifold, focusing on how the homogeneous lift of a Finsler metric influences induced and intrinsic geometric structures.

Contribution

It introduces a detailed study of the induced connections from the homogeneous prolongation of a Finsler metric to the osculator bundle, linking intrinsic and extrinsic geometries.

Findings

Derived the induced connections on the osculator bundle

Established relations between intrinsic and induced geometric objects

Analyzed the properties of the homogeneous lift of Finsler metrics

Abstract

In this article we present a study of the subspaces of the manifold OscM, the total space of the osculator bundle of a real manifold M. We obtain the induced connections of the canonical metrical N-linear connection determined by the homogeneous prolongation of a Finsler metric to the manifold OscM. We present the relation between the induced and intrinsic geometric objects of the associated osculator submanifold.