Compact homogeneous locally conformally Kahler manifolds are Vaisman. A new proof

Abstract

An LCK manifold with potential is a complex manifold with a Kahler potential on its cover, such that any deck transformation multiplies the Kahler potential by a constant multiplier. We prove that any homogeneous LCK manifold admits a metric with LCK potential. This is used to give a new proof that any compact homogeneous LCK manifold is Vaisman.

11 pages, version 2.0, the proof of Theorem 3.3 corrected and simplified

References in corpus (2)

• LCK rank of locally conformally Kahler manifolds with potential
• Positivity of LCK potential