R-Generalized and Special R-Generalized Recurrent Finsler Space

Abstract

This paper has been devoted to the study of R- generalized and special R-generalized recurrent Finsler spaces of the second order (of first and second kind). In this paper first section is introductory. In the second section we have studied curvature tensors arising from Berwald connection and Cartan connection. In the third section we have taken into account Cartan’s third curvature tensor 𝑅𝑗𝑘ℎ𝑖 and have defined R- generalized recurrent Finsler space of the second order (of first and second kinds) also we have defined special R-generalized recurrent Finsler spaces of the second order (of first and second kinds). During the course of these studies we have derived the some conditions under which R-generalized recurrent Finsler spaces and special R-generalized recurrent Finsler space of the second order of first and second kinds. In this paper we have also established the characterizing properties of generalized R- recurrent Finsler space and special R-generalized recurrent Finsler space of the second order and also we have established the conditions which Ricci tensor 𝑅𝑗𝑘 satisfies in such first and second kinds of recurrent spaces.

Keywords: R- generalized and special R-generalized recurrent Finsler spaces, Cartan’s third curvature tensor, Ricci tensor 𝑅𝑗𝑘.