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Regular version of the site

Working paper

Hopf surfaces in locally conformally Kahler manifolds with potential

Ornea L., Verbitsky M.
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.