Gicheru, James,GNgari, Cyrus, G2022-02-072022-02-072018-11-22Gicheru and Ngari; JAMCS, 30(1): 1-15, 2019; Article no.JAMCS.43211DOI: 10.9734/JAMCS/2019/43211http://repository.embuni.ac.ke/handle/embuni/3965ArticleDecomposition of recurrent curvature tensor fields of R-th order in Finsler manifolds has been studied by B. B. Sinha and G. Singh [1] in the publications del’ institute mathematique, nouvelleserie, tome 33 (47), 1983 pg 217-220. Also Surendra Pratap Singh [2] in Kyungpook Math. J. volume 15, number 2 December, 1975 studied decomposition of recurrent curvature tensor fields in generalised Finsler spaces. Sinha and Singh [3] studied decomposition of recurrent curvature tensor fields in a Finsler space. In this paper we study the Riemannian Curvature tensor with its properties its decomposition of the Riemannian curvature tensor and its properties. This raises important question: in Riemannian manifold , is it possible to decompose Riemannian curvature tensor of rank four, get another tensor of rank two and study its properties?endecomposition.Riemannian curvature tensorArticle