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Critical associated metrics on contact manifolds

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

David E. Blair
David E. Blair
Affiliation:
Department of Pure Mathematics The University of LiverpoolLiverpool, England
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Abstract

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Defining a function on the set of all Riemannian metrics associated to a contact form on a compact manifold by taking the integral of the Ricci curvature in the direction of the characteristic vector field, it is shown that on a compact regular contact manifold the only critical points of this function are the metrics for which the characteristic vector field generates a group of isometrics.

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 82 - 88
Copyright
Copyright © Australian Mathematical Society 1984

References

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