Hamiltonian mechanical systems on Para-Quaternionic Ka ̈hler Manifolds using frame fields and co-frame fields
International Journal of Development Research
Hamiltonian mechanical systems on Para-Quaternionic Ka ̈hler Manifolds using frame fields and co-frame fields
Received 19th October, 2025; Received in revised form 27th November, 2025; Accepted 17th December, 2025; Published online 30th January, 2026
Copyright©2026, Gebreel Mohammed Khur Baba Gebreel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the Hamiltonian Mechanical Systems On Para-Quaternionic Ka ̈hler Manifolds we use canonical local basis {F^*,G^*,H^* }. In this paper using frame fields i_X=X^(an+i) ∂/(∂x_(an+i) ) ,a=0 ,1 ,2 ,3 instead of the Hamiltonian vector field in the Hamiltonian Mechanical Systems On Para-Quaternionic Ka ̈hler Manifolds using frame fields and co-frame fields we verified the generalized form the Hamiltonian equation which is in conformity with the results that have obtained previously.
