The Finsler-like geometry of the (t,x)-conformal deformation of the jet Berwald-Moor metric

TL;DR

This paper develops a Finsler-like geometric framework on 1-jet spaces for a conformally deformed Berwald-Moor metric, incorporating gravitational and electromagnetic models.

Contribution

It introduces a novel Finsler-like geometry on jet spaces for the conformal deformation of the Berwald-Moor metric, including new geometric models.

Findings

Defined d-connection, d-torsions, and d-curvatures for the deformed metric

Constructed gravitational-like and electromagnetic-like geometrical models

Extended Finsler geometry to jet space with conformal deformation

Abstract

The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) attached to the (t,x)-conformal deformation of the Berwald-Moor metric.