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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

[1]Blair, D. E., Contact manifolds in Riemann geometry (Lecture Notes in Mathematics, 509, Springer, Berlin, 1976).CrossRefGoogle Scholar
[2]Blair, D. E., ‘Two remarks on contact metric structures’, Tôhoku Math. J. 29 (1977), 319–324.Google Scholar
[3]Blair, D. E. and Patnaik, J. N., ‘Contact manifolds with characteristic vector field annihilated by the curvature’, Bull. Inst. Math Acad. Sinica 9 (1981), 533–545.Google Scholar
[4]Boothby, W. M. and Wang, H. C., ‘On contact manifolds’, Ann. of Math. 68 (1958), 721–734.CrossRefGoogle Scholar
[5]Muto, Y., ‘On Einstein metrics’, J. Differential Geometry 9 (1974), 521–530.CrossRefGoogle Scholar
[6]Sasaki, S., ‘On differentiable manifolds with certain structure I’, Tôhoku Math. J. 14 (1962), 146–155.Google Scholar
[7]Sasaki, S., ‘Almost contact manifolds (Lecture Notes, Mathematical Institute, Toôhoku University, Vol1, 1965).Google Scholar