Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy

TL;DR

This paper develops a Riemann-Lagrange geometric framework on 1-jet spaces to analyze nonlinear evolution differential equations modeling economic phenomena, integrating concepts like connections, torsions, and energies.

Contribution

It introduces a novel geometric approach to study economic evolution equations using jet Riemann-Lagrange geometry, linking differential geometry with economic models.

Findings

Constructed a geometric structure on 1-jet spaces for economic DEs

Applied geometric tools to models like Kaldor and Tobin-Benhabib-Miyao

Provided insights into the geometric nature of economic dynamics

Abstract

The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.