On complex solvmanifolds and affine structures

Summary We study the problem of the existence of affine structures on compact complex solvmanifolds, in particular without the Kähler hypothesis. The main theorem gives a positive answer under a mild condition, which is true for low dimensions. A standard way to describe every solvmanifold as a quotient of (C ⁿ , *),where *is a certain Lie group structure, is also given.