On complex solvmanifolds and affine structures (Q1073225)

There is a conjecture of \textit{A. Silva} [Rend. Semin. Mat., Torino 1983, Special Issue, 172-192 (1984)] that for the class of compact complex manifolds being affine is equivalent to being a solvmanifold. In this paper the authors show the existence of affine structures on solvmanifolds which satisfy their so-called K-condition. Also they give an algorithm so that given a solvable complex Lie algebra \({\mathfrak g}\) of dimension n one can construct a product * on \({\mathbb{C}}^ n\) such that \(({\mathbb{C}}^ n,*)\) is the simply connected, connected, complex Lie group of \({\mathfrak g}\).