Cohomologically Kähler manifolds with no Kähler metrics
International Journal of Mathematics and Mathematical Sciences 2003(52) : 3315-3325 (2003)
Abstract
We show some examples of compact symplectic solvmanifolds, of
dimension greater than four, which are cohomologically
Kähler and do not admit Kähler metric since their
fundamental groups cannot be the fundamental group of any compact
Kähler manifold. Some of the examples that we study were
considered by Benson and Gordon (1990). However, whether such
manifolds have Kähler metrics was an open question. The
formality and the hard Lefschetz property are studied for the
symplectic submanifolds constructed by Auroux (1997) and some
consequences are discussed.