1-Jet Riemann-Finsler Geometry for the Three-Dimensional Time

TL;DR

This paper develops a Finsler-like geometric framework on the 1-jet space for a specific three-dimensional metric, exploring its implications for gravitational and electromagnetic field theories.

Contribution

It introduces a novel Finsler-like geometry on the 1-jet space for the rheonomic Berwald-Moor metric of order three, linking it to field theories.

Findings

Derived geometric structures including d-torsions and d-curvatures.

Formulated geometric models for gravitational and electromagnetic fields.

Extended the application of Finsler geometry to jet spaces and rheonomic metrics.

Abstract

The aim of this paper is to develop on the 1-jet space J^1(R,M^3) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric of order three. Some natural geometrical field theories (gravitational and electromagnetic) produced by the preceding rheonomic Berwald-Moor metric of order three are also exposed.