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Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 30, Issue.: 1


Decomposition of Riemannian Curvature Tensor Field and Its Properties


James Gathungu Gicheru1* and Cyrus Gitonga Ngari2

1Department of Mathematics, Ngiriambu Girls High School, P.O.Box 46-10100, Kianyaga, Kenya.

2Department of Mathematics, Computing and Information Technology, School of Pure and Applied Sciences, University of Embu, P.O.Box 6-60100, Embu, Kenya.

Article Information


(1) Dr. Dragos-Patru Covei, Professor, Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, Romania.

(2) Dr. Sheng Zhang, Professor, Department of Mathematics, Bohai University, Jinzhou, China.


(1) Bilal Eftal Acet, Adıyaman University, Turkey.

(2) Çiğdem Dinçkal, Çankaya University, Turkey.

(3) Alexandre Casassola Gonçalves,  Universidade de São Paulo, Brazil.

Complete Peer review History: http://www.sciencedomain.org/review-history/27899


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?

Keywords :

Riemannian curvature tensor; decomposition.

Full Article - PDF    Page 1-15

DOI : 10.9734/JAMCS/2019/43211

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