Symplectically aspherical manifolds with nontrivial π2 and with no Kähler metrics.

Abstract

In a previous paper, the authors show some examples of compact symplectic solvman-ifolds, of dimension six, which are cohomologically KÄahler and they do not admit Kahler metrics because their fundamental groups cannot be the fundamental group of any compact Kahler manifold. Here we generalize such manifolds to higher dimension and, by using Au-roux symplectic submanifolds [3], we construct four-dimensional symplectically aspherical manifolds with nontrivial ¼2 and with no Kahler metrics.