Bio
Gebreel Mohammed Khur Baba Gebreel is a mathematician affiliated with the Department of Mathematics, Faculty of Education at West Kordufan University in Khartoum, Sudan. His research focuses on advanced topics in differential geometry and mathematical physics, including Lagrangian dynamical systems on Clifford-Kähler manifolds, symplectic mechanics, and conformal Euler-Lagrangian equations on para-quaternionic manifolds. He has published several papers in these areas, often collaborating with colleagues such as Mohammed Ali Bashir. Gebreel also serves as a reviewer for the Global Journal of Science Frontier Research (GJSFR) and has contributed to the academic community through his editorial and peer review activities.
Educational Journey
West Kordufan University
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Experience
Research
On a New Conformal Euler-Lagrangian Equations on Para-Quaternionic Manifolds
In this paper we obtain Euler-Lagrange equations for quantum and classical mechanics by means of a canonical local basis {ð‘ð‘, ð‘®ð‘®} of V that they defined on a generalized quaternionic ð‘²ð‘²ð’‚ð’‚̈ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ manifold (M, g, V).
On the Standard Cliffordian Hamiltonian Formulation of Symplectic Mechanics Using Frame and Co-Frame fields
In the standard Cliffordian Hamiltonian mechanics we use canonical local basis {ð‘±ð‘±ðŸðŸâˆ— ,ð‘±ð‘±ðŸðŸâˆ— ,ð‘±ð‘±ðŸ‘ðŸ‘∗ }. In this paper using the frame fields ð’Šð’Šð‘¿ð‘¿=ð‘¿ð‘¿ð’‚ð’‚ð’‚ð’‚+ð’Šð’Šððððð’™ð’™ð’‚ð’‚ð’‚ð’‚+ð’Šð’Š ,ð’‚ð’‚=ðŸŽðŸŽ,ðŸðŸ,ðŸðŸ,…,ðŸ•ðŸ• instead of the Hamiltonian vector field in the Cliffordian Hamiltonian formulation we verified the generalized form of Hamiltonian equation which is in conformity with the results that have been obtained previously.
On a New Mechanics Systems on the Standard Cliffordian Kahler Manifolds using a Canonical Local Basis
In this paper we obtained a canonical local basis {
Lagrangian Dynamical Systems on Clifford Ka Ihler Manifolds
In his paper we obtained a canonical local basis {ð½ð½ð‘–} ,ð‘–ð‘–=1,5 of vector bundle 𑉠on Clifford ð¾ð‘ŽÌˆâ„Žð‘™er manifold (ð‘€,ð‘‰). The paths of semispray on Clifford ð¾ð‘ŽÌˆâ„Žð‘™er manifold are infact the solutions of Euler-Lagrange equations.
