IJPAM: Volume 108, No. 2 (2016)

ON LINEAR CONNECTION RELATING TO
A GIVEN CURVATURE

H. Ratovoarimanana$^1$, H.S.G. Ravelonirina$^2$
$^{1,2}$Department of Mathematics and Computer Science
Faculty of Science
University of Antananarivo, BP 906
Antananarivo 101, MADAGASCAR

Abstract. We study the existence and the behavior of a linear connection from a curvature given in a $n$-dimensional riemannian manifold $M$. For a polynomial section of the dual space of $TM$ on $\mathbb{R}^{n}$, in particular, we find that there is a polynomial linear connection on $\mathbb{R}^{n}$. We prove that if the nullity space of the Ricci tensor is equal to that of the curvature, then the Ricci tensor and the curvature coincide.

Received: March 17, 2016

Revised: March 17, 2016

Published: October 1, 2016

AMS Subject Classification: 53-XX, 53B05, 53C44, 17B66

Key Words and Phrases: Riemannian manifolds, linear connection, curvature, Lie algebra
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DOI: 10.12732/ijpam.v108i2.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 263 - 273


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