International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3315-3325
doi:10.1155/S0161171203211327
Cohomologically Kähler manifolds with no Kähler metrics
1Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, Bilbao 48080, Spain
2Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid 28049, Spain
Received 20 November 2002
Copyright © 2003 Marisa Fernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.