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Recurrent tensors and holonomy group

Published online by Cambridge University Press:  17 April 2009

D.K. Datta
D.K. Datta
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, USA and Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Let M be a connected C∞. A method is being introduced here to study the action of the holonomy group and the restricted holonomy group of Γ on a recurrent tensor. The main result of this paper is that if the recurrence covector W of a recurrent tensor S on M is an exact form then the tensor S is invariant under the holonomy group of Γ and if W is a closed form then S is invariant under the restricted holonomy group of Γ. In the last section, this result is applied to some particular cases including the case of a riemannian manifold with recurrent curvature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 71 - 77
Copyright
Copyright © Australian Mathematical Society 1974

References

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