Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups

Preprint number: CP3-Origins-2009-22
Authors: Thomas Bruun Madsen (CP3-Origins) and Andrew Swann (CP3-Origins)
External link: arXiv.org

A strong KT (SKT) manifold consists of a Hermitian structure whose torsion three-form is closed. We classify the invariant SKT structures on four-dimensional solvable Lie groups. The classification includes solutions on groups that do not admit compact four-dimensional quotients. It also shows that there are solvable groups in dimension four that admit invariant complex structures but have no invariant SKT structure.