Conformal classification of (k, μ)-contact manifolds

Sharma, Ramesh; Vrancken, Luc

Kodai Math. J., Tome 33 (2010) no. 1, p. 267-282 / Harvested from Project Euclid

Résumé

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.

Publié le : 2010-06-15
Classification:

@article{1278076342,
     author = {Sharma, Ramesh and Vrancken, Luc},
     title = {Conformal classification of (k, $\mu$)-contact manifolds},
     journal = {Kodai Math. J.},
     volume = {33},
     number = {1},
     year = {2010},
     pages = { 267-282},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1278076342}
}

Sharma, Ramesh; Vrancken, Luc. Conformal classification of (k, μ)-contact manifolds. Kodai Math. J., Tome 33 (2010) no. 1, pp.  267-282. http://gdmltest.u-ga.fr/item/1278076342/