Decomposition of Riemannian Curvature Tensor Field and Its Properties
James Gathungu Gicheru, Cyrus Gitonga Ngari
Journal of Advances in Mathematics and Computer Science · pp. 1–15 · Published 21 Dec 2018
10.9734/JAMCS/2019/43211Abstract
Decomposition 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?
Cited by 2
Sukh Pal Singh, Indiwar Singh Chauhan, T.S. Chauhan · Ain Shams Engineering Journal · 2025
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