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arXiv · 1601.07421

Hopf surfaces in locally conformally Kahler manifolds with potential

Liviu Ornea·Misha Verbitsky
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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 complex surface with normalization biholomorphic to a Hopf surface H. Moreover, H can be chosen non-diagonal, hence, also not admitting a Vaisman structure.

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Liviu Ornea, Misha Verbitsky. 2016-01-27. Hopf surfaces in locally conformally Kahler manifolds with potential. https://doi.org/10.1007/s10711-019-00495-5

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