Geometrical Objects on the First Order Jet Space $J^1(T,R^5)$ Produced by the Lorenz Atmospheric DEs System

TL;DR

This paper constructs geometric objects on the 1-jet space associated with the Lorenz atmospheric differential equations, including connections, torsions, curvatures, and field theories, based on Euclidean metrics.

Contribution

It introduces a novel geometric framework on jet spaces derived from Lorenz system equations and Euclidean metrics, integrating connections and field theories.

Findings

Defined a non-linear connection and generalized Cartan connection.

Derived d-torsions and d-curvatures related to the Lorenz system.

Formulated a jet electromagnetic field and Yang-Mills energy.

Abstract

The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where $T/subset R$, like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atmospheric DEs system and the pair of Euclidian metrics $/Delta = (1,/delta_{ij})$ on $T/times R^5$.