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A Variational Characterization of Contact Metric Manifolds With Vanishing Torsion

Published online by Cambridge University Press:  20 November 2018

D. E. Blair  and
D. Perrone
D. E. Blair
Affiliation:
Department of Mathematics Michigan State University East Lansing, MI 48824 U.S.A.
D. Perrone
Affiliation:
Dipartimento di Matematica Facoltá di Scienze Universitá Degli Studi di Lecce Via Arnesano 73100 Lecce, Italy
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Abstract

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Chern and Hamilton considered the integral of the Webster scalar curvature as a functional on the set of CR-structures on a compact 3-dimensional contact manifold. Critical points of this functional can be viewed as Riemannian metrics associated to the contact structure for which the characteristic vector field generates a 1-parameter group of isometries i.e. K-contact metrics. Tanno defined a higher dimensional generalization of the Webster scalar curvature, computed the critical point condition of the corresponding integral functional and found that it is not the K-contact condition. In this paper two other generalizations are given and the critical point conditions of the corresponding integral functionals are found. For the second of these, this is the K-contact condition, suggesting that it may be the proper generalization of the Webster scalar curvature.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 455 - 462
Copyright
Copyright © Canadian Mathematical Society 1992

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