Solvmanifold

Summary

A solvmanifold is a homogeneous space $G/H$ of a connected solvable Lie group $G$ by a closed subgroup $H$. Tori, nilmanifolds and many mapping tori of torus maps are solvmanifolds. The compact ones of the form $G/\Gamma$, with $\Gamma$ a lattice, are natural test spaces in geometry and dynamics. For example, they give examples of symplectic manifolds without Kähler structure.