Synge-Beil and Riemann-Jacobi jet structures with applications to physics

Abstract

In the framework of geometrized first-order jet approach, we study the Synge-Beil generalized Lagrange jet structure, derive the canonic nonlinear and Cartan connections, and infer the Einstein-Maxwell equations with sources; the classical ansatz is emphasized as a particular case. The Lorentz-type equations are described and the attached Riemann-Jacobi structures for two certain uniparametric cases are presented.