Journal of Lie Theory 21 (2011), No. 1, 055--070
Copyright Heldermann Verlag 2011
Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups
Thomas Bruun Madsen
Dept. of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
tbmadsen@imada.sdu.dk
Andrew Swann
Dept. of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
swann@imada.sdu.dk
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.
Keywords: Hermitian metric, complex structure, strong KT geometry, Kaehler with torsion, solvable Lie group.
MSC: 53C55; 53C30, 32M10
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