In mathematics, a solvmanifold is a homogeneous space of a connected solvable Lie group. It may also be characterized as a quotient of a connected solvable Lie group by a closed subgroup. (Some authors also require that the Lie group be simply-connected, or that the quotient be compact.) A special class of solvmanifolds, nilmanifolds, was introduced by Anatoly Maltsev, who proved the first structural theorems. Properties of general solvmanifolds are similar, but somewhat more complicated.