P-third order generalized Finsler space in the Berwald sense

Abstract

The generalized recurrent and birecurrent spaces for Pijkh are discussed by Finslerian geometrics. Now, in this paper, we generalize these spaces by using the covariant derivative of third order in the sense of Berwald. The necessary and sufficient condition for Pijkh satisfying the generalized trirecurrence property is obtained. In addition, we show that the covariant derivative in the sense of Berwald coincides with the h-covariant derivative in the sense of Cartan. Various identities concerning such space are established.