International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3315-3325

Cohomologically Kähler manifolds with no Kähler metrics

Marisa Fernández,1 Vicente Muñoz,2 and José A. Santisteban1

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.


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.