28 apr 2022 -- 14:30
Aula Tricerri, DIMaI, Firenze & online
Seminari di Geometria del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze
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.