Jet Riemann-Lagrange Geometry and Some Applications in Theoretical Biology

TL;DR

This paper develops a Riemann-Lagrange geometric framework on 1-jet spaces to analyze biological models like cancer and HIV infection, integrating geometric structures with differential equations.

Contribution

It introduces a novel geometric approach on jet spaces for biological systems, linking differential geometry with biological modeling.

Findings

Constructed Riemann-Lagrange geometry on 1-jet spaces.

Applied geometric structures to biological models.

Provided insights into biological phenomena via geometric methods.

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 electromagnetic Yang-Mills energies, starting from some given nonlinear evolution ODEs systems modelling biologic phenomena like the cancer cell population model or the infection by human immunodeficiency virus-type 1 (HIV-1) model.