Locally conformal symplectic nilmanifolds with no locally conformal   K\"ahler metrics
  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. 
Giovanni Bazzoni, Juan Carlos Marrero
math.DG math.SG