Energy β-Conformal Change and Special Finsler Spaces
Affiliation(s)
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. Department of Mathematics, Taif University, Makkah, KSA.
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. Department of Mathematics, Taif University, Makkah, KSA.
ABSTRACT
The main aim of the present paper is to establish an intrinsic investigation of the energy β-conformal change of the most important special Finsler spaces, namely, Ch-recurrent, Cv-recurrent, C0-recurrent, Sv-recurrent, quasi-C-reducible, semi-C-reducible, C-reducible, P-reducible, C2-like, S3-like, P2-like and h-isotropic, ···, etc. Necessary and sufficient conditions for such special Finsler manifolds to be invariant under an energy β-conformal change are obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.
Cite this paper
A. Soleiman and A. Ishan, "Energy β-Conformal Change and Special Finsler Spaces," Journal of Modern Physics, Vol. 4 No. 7, 2013, pp. 983-990. doi: 10.4236/jmp.2013.47132.
A. Soleiman and A. Ishan, "Energy β-Conformal Change and Special Finsler Spaces," Journal of Modern Physics, Vol. 4 No. 7, 2013, pp. 983-990. doi: 10.4236/jmp.2013.47132.
References
[1] T. Mestdag and V. Toth, Report Mathmatics Physics, Vol. 50, 2002, pp. 167-193. doi:10.1016/S0034-4877(02)80053-2 [2] A. Soleiman, International Journal of Geometric Methods in Modern Physic, Vol. 9, 2012, 21 p. [3] H. Akbar-Zadeh, “Initiation to Global Finsler Geometry,” Elsevier, San Diego, 2006. [4] P. Dazord, “Propriétés Globales des Géodésiques des Espaces de Finsler,” Thése d’Etat, Publication Department Mathematics Lyon, 1969. [5] A. A. Tamim, “General Theory of Finsler Spaces with Applications to Randers Spaces,” Ph.D. Thesis, Cairo University, Cairo, 1991. [6] N. L. Youssef, S. H. Abed and A. Soleiman, Balkan Journal of Geometry and Its Applications, Vol. 15, 2010, pp. 138-150. [7] N. L. Youssef, S. H. Abed and A. Soleiman, Tensor N. S., Vol. 71, 2009, pp. 187-208. [8] N. L. Youssef, S. H. Abed and A. Soleiman, Algebras, Groups and Geometries, Vol. 25, 2008, pp. 363-386. [9] F. Brickell, Proceedings of the American Mathematical Society, Vol. 16, 1965, pp. 90-191. [10] J. Grifone, Annales de L’Institut Fourier, Grenoble, Vol. 22, 1972, pp. 287-334. doi:10.5802/aif.407 [11] J. Grifone, Annales de L’Institut Fourier, Grenoble, Vol. 22, 1972, pp. 291-338. doi:10.5802/aif.431 [12] J. Klein and A. Voutier, Annales de L’Institut Fourier, Grenoble, Vol. 18, 1968, pp. 241-260. doi:10.5802/aif.282 [13] N. L. Youssef, Tensor, N. S., Vol. 36, 1982, pp. 275-280. [14] N. L. Youssef, S. H. Abed and A. Soleiman, Kyoto Journal of Mathematics, Vol. 48, 2008, pp. 857-893. [15] N. L. Youssef, S. H. Abed and A. Soleiman, International Journal of Geometric Methods in Modern Physics, Vol. 6, 2009, pp. 1003-1031. [16] N. L. Youssef, S. H. Abed and A. Soleiman, Journal of the Egyptian Mathematical Society, Vol. 18, 2010, pp. 67-90.
[1] T. Mestdag and V. Toth, Report Mathmatics Physics, Vol. 50, 2002, pp. 167-193. doi:10.1016/S0034-4877(02)80053-2 [2] A. Soleiman, International Journal of Geometric Methods in Modern Physic, Vol. 9, 2012, 21 p. [3] H. Akbar-Zadeh, “Initiation to Global Finsler Geometry,” Elsevier, San Diego, 2006. [4] P. Dazord, “Propriétés Globales des Géodésiques des Espaces de Finsler,” Thése d’Etat, Publication Department Mathematics Lyon, 1969. [5] A. A. Tamim, “General Theory of Finsler Spaces with Applications to Randers Spaces,” Ph.D. Thesis, Cairo University, Cairo, 1991. [6] N. L. Youssef, S. H. Abed and A. Soleiman, Balkan Journal of Geometry and Its Applications, Vol. 15, 2010, pp. 138-150. [7] N. L. Youssef, S. H. Abed and A. Soleiman, Tensor N. S., Vol. 71, 2009, pp. 187-208. [8] N. L. Youssef, S. H. Abed and A. Soleiman, Algebras, Groups and Geometries, Vol. 25, 2008, pp. 363-386. [9] F. Brickell, Proceedings of the American Mathematical Society, Vol. 16, 1965, pp. 90-191. [10] J. Grifone, Annales de L’Institut Fourier, Grenoble, Vol. 22, 1972, pp. 287-334. doi:10.5802/aif.407 [11] J. Grifone, Annales de L’Institut Fourier, Grenoble, Vol. 22, 1972, pp. 291-338. doi:10.5802/aif.431 [12] J. Klein and A. Voutier, Annales de L’Institut Fourier, Grenoble, Vol. 18, 1968, pp. 241-260. doi:10.5802/aif.282 [13] N. L. Youssef, Tensor, N. S., Vol. 36, 1982, pp. 275-280. [14] N. L. Youssef, S. H. Abed and A. Soleiman, Kyoto Journal of Mathematics, Vol. 48, 2008, pp. 857-893. [15] N. L. Youssef, S. H. Abed and A. Soleiman, International Journal of Geometric Methods in Modern Physics, Vol. 6, 2009, pp. 1003-1031. [16] N. L. Youssef, S. H. Abed and A. Soleiman, Journal of the Egyptian Mathematical Society, Vol. 18, 2010, pp. 67-90.