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

## Original-research-article

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

Editor(s):

(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.

Reviewers:

(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

Abstracts

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.

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