CERTAIN TYPES OF K^h-BIRECURRENT FINSLER SPACE(I)

Abstract

        H.D. Pande and B. Singh [21] discussed the recurrency in an affinely connected space. P.K. Dwivedi [6] worked out the role of -reducible space in affinely connected space. A.A.A. Muhib [20] obtained some results when -generalized trirecurrent and special  generalized trirecurrent spaces are affinely connected spaces. A.A. M. Saleem [24] obtained some results when the -recurrentin -generalized birecurrent and -special  generalized birecurrent are affinely connected spaces.

         A Landsberg space of dimension  was first considered by G. Landsberg [14] from a  standpoint of variation. As to such spaces  of  many  dimensions, É. Cartan [5] introduced  it as one of particular cases and further  L. Berwald ([2],[3]) showed that the space was  characterized by  , where    is the (hv)-curvature tensor. H. Yasuda [26] gave  other characterizations of a Landsberg space and contributed a little to the theory of  Landsberg spaces. R. Verma [25] obtained the condition of a P-reducible -recurrent  space be a necessarily a Landsberg space. A.A.M. Saleem [24] obtained some results  when the -recurrentin -generalized birecurrent and -special generalized birecurrent spaces are Landsberg spaces. P.K. Dwivedi [6] worked out the role of   -reducible  space in  Landsberg  space .

        In this paper we use the property of -BR-  in affinely connected space and Landsberg space. We have obtained different

theorems for some  tensors to be satisfying the conditions of the above spaces and we have obtained various  identities in such spaces.