Abstract: In the present paper, a Finsler space whose curvature tensor R_jkh^i satisfies R_(jkh׀l׀m)^i= 〖 a〗_lm R_jkh^i+〖 b〗_lm (δ_k^i g_jh-δ_h^i g_jk ) ,R_jkh^i≠ 0 , where 〖 a〗_lm and 〖 b〗_lm are non-zero covariant tensor fields of second order called recurrence tensor fields, is introduced, such space is called as a generalized R^h-birecurrent Finsler space . The associate tensor R_jrkh of Cartan's third curvature tensor R_jkh^i , the torsion tensor H_kh^i ,the deviation tensor R_h^i, the Ricci tensor R_jk, the vector H_k and the scalar curvature R of such space are non-vanishing. Under certain conditions, a generalized R^h-birecurrent Finsler space becomes Landsberg space . Some conditions have been pointed out which reduce a generalized R^h-birecurrent Finsler space F_n (n>2) into Finsler space of scalar curvature.
Keywords: Finsler space; Generalized R^h-birecurrent Finsler space; Ricci tensor; Landsberg space; Finsler space of scalar curvature.
Title: On a Generalized R^h- Birecurrent Finsler Space
Author: Fahmi Y.A. Qasem, Wafa`a H.A. Hadi
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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