Invariant strong KT geometry on four-dimensional solvable Lie groups

Details Invariant strong KT geometry on four-dimensional solvable Lie groups Invariant strong KT geometry on four-dimensional solvable Lie groups

2009-11-03

arxiv.org/abs/0911.0535v1

Mathematics

Differential Geometry

17 pages

Scientific paper

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.

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