Conformal vector fields on lcK manifolds

Abstract: It is well known that on compact Kähler manifolds every conformal vector field is Killing (Lichnerowicz) and every Killing vector field is holomorphic. In this talk I will extend these results to the locally conformally Kähler setting. More precisely, I will show that any conformal vector field $\xi$ on a compact lcK manifold is Killing with respect to the Gauduchon metric, and if the Kähler cover of the manifold is neither flat, nor hyperkähler, then $\xi$ is holomorphic. This is joint work with Mihaela Pilca.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.