A six dimensional compact symplectic solvmanifold without Kähler structures

Marisa Fernandez (1) , Manuel de Leon (2) , Martintxo Saralegi-Aranguren (3)

1 Departamento de Matemáticas
2 IMFF - Instituto de Matemáticas y Física Fundamental
3 LML - Laboratoire de Mathématiques de Lens

The purpose of this paper is to construct a compact symplectic (non-nilpotent) solvmanifold $M^{6} = \Gamma / G$ of dimension $6$ which does not admit Kähler structures. We show that the minimal model of $M^{6}$ is not formal by proving that there are non-trivial (quadruple) Massey products, however we remark that all the (triple) Massey products of $M^{6}$ vanish.

Domaines: Géométrie différentielle [math.DG]

Marisa Fernandez, Manuel de Leon, Martintxo Saralegi-Aranguren. A six dimensional compact symplectic solvmanifold without Kähler structures. Osaka Journal of Mathematics, 1996, 33, pp.19-35. ⟨hal-00870082⟩