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Certain Characteristics of the Curvature Tensor of an Affinely Connected Manifold

Published online by Cambridge University Press:  20 November 2018

Ramesh Sharma
Ramesh Sharma*
Affiliation:
Department of Mathematics, University of WindsorOntario N9B 3P4, Canada
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Abstract

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We show how flatness and symmetry of an affinely connected manifold relate themselves to the symmetry of the curvature tensor and its covariant derivative in certain slots. Then we reduce Bianchi first identity to the same form as when the connexion is symmetric; even when the connexion is non-symmetric by considering other conditions.

Keywords

53C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 355 - 357
Copyright
Copyright © Canadian Mathematical Society 1983

References

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3. Sasaki, S., Almost contact manifolds. I. Lecture note). Mathematical Institute, Tohoku University (1965).Google Scholar