Some Identities for Generalized Curvature Tensors in ?-Recurrent Finsler Space

The purpose of the present paper is to consider and study a certain identities for some generalized curvature tensors in ℬ-recurrent Finsler space ?? in which Cartan’s second curvature tensor ???ℎ? satisfies the generalized of recurrence condition with respect to Berwald’s connection parameters G?ℎ? which given by the condition ℬ????ℎ?=?? ???ℎ?+??( ?ℎ? ???− ??? ??ℎ), where ℬ? is covariant derivative of first order (Berwald’s covariant differential operator ) with respect to ??, it’s called a generalized ℬP-recurrent space. We shall denote it briefly by ?ℬ?-???. We have obtained Berwald’s covariant derivative of first order for the h(v)-torsion tensor ??ℎ ?, the deviation tensor ?ℎ ? and the covariant derivative of the tensor ???.ℎ (in the sense of Berwald), also we find some theorems of the R-Ricci tensor ??? and the curvature vector ??in our space. We obtained the necessary and sufficient condition for Berwald’s covariant derivative of Weyl’s projective curvature tensor ???ℎ? and its torsion tensor ??ℎ? in our space. Also, we have proved that in ?ℬ?-???, Cartan’s second curvature tensor ???ℎ? and the v(hv)-torsion tensor ??ℎ? for ?=4 .

Keywords:

Finsler space, Cartan’s second curvature tensor ???ℎ?, Generalized ℬ?-recurrent space, Weyl’s projective curvature tensor ???ℎ? Cartan’s fourth curvature tensor ???ℎ?,

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Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

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