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Conditions for an affine manifold with torsion to have a Riemann–Cartan structure*
Published online by Cambridge University Press: 24 October 2008
Abstract
Necessary and sufficient conditions for the local existence of a metric compatible with the affine connection are obtained in terms of the Riemann tensor and its first-order covariant derivatives in a generic affine manifold with torsion. In case these conditions are satisfied, the solutions of the metric are given in terms of integrals and are unique up to a constant scale factor. Some global conditions are also obtained and discussed.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 517 - 527
- Copyright
- Copyright © Cambridge Philosophical Society 1981
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