Let G be a complex, connected, simply connected, solvable Lie group and U a discrete uniform subgroup. The authors give a sufficient condition, in terms of structure constants of the Lie algebra of G, under which the complex solvmanifold M = G/U has an analytic affine structure (i.e., there is an atlas on M whose transition functions are affine). The condition is fulfilled for all solvmanifolds M = G/U of dimension ≤ 5.
On Complex Solvmanifolds and Affine Structures / L. Alessandrini; M. Andreatta. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 142(1985), pp. 351-370.
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