Finsler Space of Fourth Order on Some Properties of Rh-Generalized Recurrent

Abstract

In the present  paper‚ a Finsler space  whose Cartan’s fourth curvature tensor R_jkh^i satisfies R_(jkh|l|m|n|s)^i=c_(lmns R_jkh^i+d_lmns δ_h^i g_jk) , R_jkh^i  ≠ 0  , where ׀l׀m|n|s  is h-covariant derivative of fourth order ( Cartan’s third kind covariant differential operator ), with respect to  x^l  , x^m  , x^n and x^s successively, c_(lmns ) and d_(lmns ) are non-zero covariant vector field and covariant tensor field of third order, respectively‚ is introduced and  such space is called as R^h -generalized fourecurrent Finsler space and we denote them briefly by R^h-G-FR  f_n‚ we obtained some generalized fourecurrent space. Also we introduced Ricci generalized fourecurrent space.