Marisa Fernández, Vicente Muñoz, José A. Santisteban, "Cohomologically Kähler manifolds with no Kähler metrics", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 954357, 11 pages, 2003. https://doi.org/10.1155/S0161171203211327
Cohomologically Kähler manifolds with no Kähler metrics
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.
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