# Hopf surfaces in locally conformally Kahler manifolds with potential

Research paper by Liviu Ornea, Misha Verbitsky

Indexed on: 01 Feb '16Published on: 01 Feb '16Published in: Mathematics - Algebraic Geometry

#### Abstract

An LCK manifold with potential is a compact quotient $M$ of a Kahler manifold $X$ equipped with a positive plurisubharmonic function $f$, such that the monodromy group acts on $X$ by holomorphic homotheties and maps $f$ to a function proportional to $f$. It is known that $M$ admits an LCK potential if and only if it can be holomorphically embedded to a Hopf manifold. We prove that any non-Vaisman LCK manifold with potential contains a Hopf surface $H$. Moreover, $H$ can be chosen non-diagonal, hence, also not admitting a Vaisman structure.