I. Wanas, M.E. Kahil, M.2020-01-182020-01-182005[1] Wanas, M.I., Melek, M. and Kahil, M.E.(1995) Astrophys. Space Sci.,228, 273. ; gr-qc/0207113. [2] Wanas, M.I.(1998) Astrophys. Space Sci., 258, 237 ; gr-qc/9904019. [3] Wanas, M.I., Melek, M. and Kahil, M.E. (2000) Grav. Cosmol., 6 , 319. [4] Wanas, M.I., Melek, M. and Kahil, M.E. (2002) Proc. MG IX, part B, p.1100, Eds. V.G. Gurzadyan et al. (World Scientific Pub.); gr-qc/0306086. [5] Adler, R. Bazin, M. and Schiffer, M. (1975) ”Introduction to General Relativity”, McGraw Hill. [6] Eisenhart, L.P. (1926) ”Riemannian Geometry”, Princeton Univ. Press. [7] Bazanski, S.I. (1989) J. Math. Phys., 30, 1018. [8] Wanas, M.I. and Kahil, M.E.(1999) Gen. Rel. Grav., 31, 1921. ; gr-qc/9912007 10 [9] Mikhail, F.I. and Wanas, M.I. (1977) Proc. Roy. Soc. Lond. A 356, 471. [10] Wanas, M.I. (2001) Stud. Cercet. S¸tiint¸. Ser. Mat. Univ. Bac˘au 10, 297; gr-qc/0209050 [11] Wanas, M.I. (2000) Turk. J. Phys., 24, 473 ; gr-qc/0010099. [12] Straumann, N. (1984) ”General Relativity and Relativistic Astrophysics”, Springer-Verlag. [13] Wanas, M.I. (2003) Algebras, Groups and Geometries, 20, 345a. [14] Aharanov, Y. and Bohm, D. (1959) Phys. Rev. 115, 485. [15] Peshkin, M. (1981) Physics Reports, 6, 375.https://arxiv.org/pdf/gr-qc/0408029.pdfMSA Google ScholarIn the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov-Bohm effect. It is to be considered that all extra terms will vanish if the space-time used is torsion-less.enUniversity of Path equationsArticle