Decomposition of Curvatur tensor filed \(R_jkh^i \) recurrent spaces of first and second order

Abstract

Finsler geometry has many uses in relative physics and many of mathematicians contributed in this study and improved it. Takano [26] has studied the decomposition of curvature tensor in a recurrent space. Sinha and Singh [25] have studied and defined the decomposition of recurrent curvature tensor field in a Finsler space. Negi and Rawat [11] and [12] have studied decomposition of recurrent curvature tensor fields in K¨aehlerian space. Rawat and Silswal [19] studied and defined the decomposition of recurrent curvature tensor fields in a Tachibana space. Rawat and Singh [21] studied the decomposition of curvature tensor field in K¨aehlerian recurrent space of first order. Further, Rawat and others [20],[22] and [23] studied the decomposition of curvature tensor field in Einstein- K¨aehlerian recurrent space of first order. Al-Qashbari [1], [2], [3] and [4] and Qasem and others [14], [15], [16], [17] and [18] studied the recurrent for different curvature tensors .In the present paper, we have studied the decomposition of curvature tensor fields \(R_jkh^i\) in recurrent space of First order and second order, and several theorems have been established and proved.