Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics

Abstract

We report on a question, posed by L. Ornea and M. Verbitsky in [32], about examples of compact locally conformal symplectic manifolds without locally conformal Kähler metrics. We construct such an example on a compact 4-dimensional nilmanifold, not the product of a compact 3-manifold and a circle.

Keywords

• locally conformal symplectic manifolds
• locally conformal kähler manifolds
• compact nilmanifolds
• 53d05
• 53c55