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June 2010 Conformal classification of (k, μ)-contact manifolds
Ramesh Sharma, Luc Vrancken
Kodai Math. J. 33(2): 267-282 (June 2010). DOI: 10.2996/kmj/1278076342

Abstract

First we improve a result of Tanno that says "If a conformal vector field on a contact metric manifold M is a strictly infinitesimal contact transformation, then it is an infinitesimal automorphism of M" by waiving the "strictness" in the hypothesis. Next, we prove that a (k, μ)-contact manifold admitting a non-Killing conformal vector field is either Sasakian or has k = –n – 1, μ = 1 in dimension > 3; and Sasakian or flat in dimension 3. In particular, we show that (i) among all compact simply connected (k, μ)-contact manifolds of dimension > 3, only the unit sphere S2n+1 admits a non-Killing conformal vector field, and (ii) a conformal vector field on the unit tangent bundle of a space-form of dimension > 2 is necessarily Killing.

Citation

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Ramesh Sharma. Luc Vrancken. "Conformal classification of (k, μ)-contact manifolds." Kodai Math. J. 33 (2) 267 - 282, June 2010. https://doi.org/10.2996/kmj/1278076342

Information

Published: June 2010
First available in Project Euclid: 2 July 2010

zbMATH: 1194.53041
MathSciNet: MR2681540
Digital Object Identifier: 10.2996/kmj/1278076342

Rights: Copyright © 2010 Tokyo Institute of Technology, Department of Mathematics

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Vol.33 • No. 2 • June 2010
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