Jet Geometrical Objects Produced by Linear ODEs Systems and Superior Order ODEs

TL;DR

This paper develops a Riemann-Lagrange geometric framework on 1-jet spaces derived from linear ODE systems and higher-order ODEs, incorporating concepts like d-connections, torsions, curvatures, and electromagnetic fields.

Contribution

It introduces a novel geometric approach to analyze linear and higher-order ODEs using jet space structures and electromagnetic field concepts.

Findings

Constructed Riemann-Lagrange geometry on 1-jet spaces from ODEs

Defined electromagnetic d-field and Yang-Mills energy in this geometric context

Extended the framework to non-homogeneous higher-order linear ODEs

Abstract

The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given linear ODEs system or a given superior order ODE. The case of a non-homogenous linear ODE of superior order is disscused.