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
Marisa Fernández1
, Vicente Muñoz2
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
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.