Abstract

In this paper we defined \(K^h\)-birecurrent space which is characterized by the condition\(K_jkh|m|l^i=a_lm K_jkh^i\) , \(K_jkh^i≠0\), also we introduced some decompositions of Cartan's fourth and third curvature tensor and Berwald curvature tensor and its torsion tensor. The aim of this paper is devoted to the discussion of decomposition for different tensors in \(K^h\)-birecurrent space and \(K^h\)-birecurrent affinely connected space and the decomposition of curvature tensor Cartan's fourth and third in \(K^h\)-birecurrent space, also the decomposition of curvature tensor of Berwald in \(K^h\)-birecurrent affinely connected space, various results, formulas, theorems and different identities have been obtained.