On complex solvmanifolds and affine structures
Copyright policy )On complex solvmanifolds and affine structures
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 \({\mathfrak g}\).
- University of Parma Italy
- University of Trento Italy
Nilpotent and solvable Lie groups, Affine differential geometry, Homogeneous complex manifolds, 540, Complex Lie groups, group actions on complex spaces, K- condition, solvable complex Lie algebra, 510, affine compact complex manifold, affine structures on solvmanifolds, Compact analytic spaces
Nilpotent and solvable Lie groups, Affine differential geometry, Homogeneous complex manifolds, 540, Complex Lie groups, group actions on complex spaces, K- condition, solvable complex Lie algebra, 510, affine compact complex manifold, affine structures on solvmanifolds, Compact analytic spaces
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