Dual jet geometrical objects of momenta in the time-dependent Hamilton geometry

TL;DR

This paper develops the fundamental geometric structures on the dual 1-jet space for time-dependent Hamiltonian systems, including tensors, semisprays, and connections, to advance the mathematical framework of jet geometry.

Contribution

It introduces and formalizes key geometric objects like distinguished tensors and nonlinear connections on the dual jet space for time-dependent Hamiltonian systems.

Findings

Defined dual jet geometrical objects for Hamiltonian systems.

Established relations among tensors, semisprays, and connections.

Enhanced the mathematical tools for analyzing time-dependent Hamiltonian dynamics.

Abstract

The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.