Lagrangian and Hamiltonian Mechanical Systems on Para-Quaternionic Kaehler Manifolds

TL;DR

This paper develops a geometric framework for Lagrangian and Hamiltonian mechanics on para-quaternionic Kaehler manifolds, extending classical mechanics into a new geometric setting with potential physical applications.

Contribution

It introduces para-quaternionic Kaehler analogues of Lagrangian and Hamiltonian systems, providing a novel geometric approach to these classical mechanics frameworks.

Findings

Formulation of Lagrangian systems on para-quaternionic Kaehler manifolds

Formulation of Hamiltonian systems on para-quaternionic Kaehler manifolds

Derivation of geometrical-physical results for these systems

Abstract

In the present paper, we introduce para-quaternionic Kaehler analogue of Lagrangian and Hamiltonian mechanical systems. Finally, the geometrical-physical results related to para-quaternionic Kaehler mechanical systems are also given.