Certain Identities in Generalized Rh Recurrent Finsler Space

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Year:
2016
Type of Publication:
Article
Keywords:
Finsler space, Generalized Rh Recurrent Space, Ricci Tensor
Authors:
Fahmi Yaseen Abdo Qasem; Adel Mohammed Ali AL-Qashbari
Journal:
IJISM
Volume:
4
Number:
2
Pages:
66-69
Month:
March
ISSN:
2347-9051
Abstract:
In this paper we define a Finsler space F_n in which Cartan's third curvature tensor R_jkh^i satisfies the generalized of recurrence condition with respect to Cartan’s convection parameters _kh^(*i) which given by the condition R_(jkh׀l)^i=〖λ_l R〗_jkh^i+μ_l (δ_h^i g_jk-δ_k^i g_jh ), where├ ┤|l is h-covariant differentiation, λ_l and μ_l are non-null covariant vectors field is introduced and such space is called as a generalized R^h-recurrent space and denote it briefly by G H^h-〖R F〗_n . The Ricci tensor R_kh , the curvature vector R_k and the curvature scalar R of such space are non-vanishing. Finally, we obtained certain identities for a generalized R^h-recurrent space.

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