Locally conformal symplectic nilmanifolds with no locally conformal K\"ahler metrics

TL;DR

This paper presents an example of a compact nilmanifold that has a locally conformal symplectic structure but does not admit any locally conformal Kähler metrics, answering a previously open question.

Contribution

The authors construct a specific compact nilmanifold with a locally conformal symplectic structure that cannot support any locally conformal Kähler metrics, providing a counterexample to a known question.

Findings

Existence of a compact locally conformal symplectic nilmanifold without locally conformal Kähler metrics

Answers an open question by L. Ornea and M. Verbitsky

Demonstrates limitations of compatibility between these geometric structures

Abstract

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.