A construction of compact pseudo-Kähler solvmanifolds with no Kähler structures

Abstract

In this paper we investigate the Hard Lefschetz property on certain compact symplectic solvmanifolds and constmct compact pseudo-Kähler solvmanifolds which do not have the Hard Lefschetz property. We also construct holomorphic symplectic structures, hypercomplex structures and pseudo-hyperkähler stmctures on certain compact solvmanifolds.