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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

Wei-Tou Ni
Wei-Tou Ni
Affiliation:
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China
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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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References

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