Mathematical Research Letters

Volume 30 (2023)

Number 5

Conformal vector fields on lcK manifolds

Pages: 1591 – 1608

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a12

Authors

Andrei Moroianu (Laboratoire de mathématiques d’Orsay, Université Paris-Saclay, CNRS, Orsay, France)

Mihaela Pilca (Fakultät für Mathematik, Universität Regensburg, Germany)

Abstract

We show that any conformal vector field on a compact lcK manifold is Killing with respect to the Gauduchon metric. Furthermore, we prove that any conformal vector field on a compact lcK manifold whose Kähler cover is neither flat, nor hyperkähler, is holomorphic.

Full Text (PDF format)

This work was supported by the Procope Project No. 57445459 (Germany) / 42513ZJ (France).

Received 22 July 2021

Received revised 4 January 2022

Accepted 19 January 2022

Published 14 May 2024