Author URLs
Document Type
Article
Publication Date
2010
Subject: LCSH
Contact transformations, Vector fields, Contact manifolds
Disciplines
Mathematics
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.
Repository Citation
Sharma, Ramesh and Vrancken, Luc, "Conformal Classification of (k, μ)-Contact Manifolds" (2010). Mathematics Faculty Publications. 6.
https://digitalcommons.newhaven.edu/mathematics-facpubs/6
Publisher Citation
Ramesh Sharma and Luc Vrancken. Conformal classification of (k,mu)-contact manifolds, Kodai Mathematical Journal 33 (2010), 267-282.
Comments
Open access courtesy of Kodai Mathematical Journal. Articles older than 5 years are open. Electronic access at http://projecteuclid.org/euclid.kmj/1278076342 . Journal homepage at http://www.math.titech.ac.jp/~tosho/Journal/about/index.html