Lagrangian and Hamiltonian Dynamics on Para-Kaehlerian Space Form

TL;DR

This paper develops Euler-Lagrange and Hamiltonian equations within the context of para-Kaehlerian space forms, exploring their geometric and physical implications for mechanical systems.

Contribution

It introduces a novel framework for formulating classical mechanics on para-Kaehlerian space forms, extending geometric methods to this setting.

Findings

Derived Euler-Lagrange equations on para-Kaehlerian space forms.

Formulated Hamiltonian equations in the same geometric context.

Discussed applications to geometric and physical systems.

Abstract

In this study, we introduce Euler-Lagrange and Hamiltonian equations on (R2; g; J) being a model of para-Kaehlerian Space Forms. Finally, some geometrical and physical results on the related mechanic systems have been discussed.