## Kodai Mathematical Journal

### Conformal classification of (k, μ)-contact manifolds

#### 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.

#### Article information

Source
Kodai Math. J., Volume 33, Number 2 (2010), 267-282.

Dates
First available in Project Euclid: 2 July 2010

https://projecteuclid.org/euclid.kmj/1278076342

Digital Object Identifier
doi:10.2996/kmj/1278076342

Mathematical Reviews number (MathSciNet)
MR2681540

Zentralblatt MATH identifier
1194.53041

#### Citation

Sharma, Ramesh; Vrancken, Luc. Conformal classification of ( k , μ)-contact manifolds. Kodai Math. J. 33 (2010), no. 2, 267--282. doi:10.2996/kmj/1278076342. https://projecteuclid.org/euclid.kmj/1278076342