Journal of Lie Theory

no. 1
Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups
Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 55-70
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.
DOI: 10.5802/jolt.622
Classification: 53C55, 53C30, 32M10
Keywords: Hermitian metric, complex structure, strong KT geometry, Kaehler with torsion, solvable Lie group 
@article{JOLT_2011_21_1_a1,
     author = {T. B. Madsen and A. Swann},
     title = {Invariant {Strong} {KT} {Geometry} on {Four-Dimensional} {Solvable} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {55--70},
     year = {2011},
     volume = {21},
     number = {1},
     doi = {10.5802/jolt.622},
     zbl = {1242.53093},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.622/}
}
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T. B. Madsen; A. Swann. Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups. Journal of Lie Theory, Volume 21 (2011) no. 1, pp. 55-70. doi: 10.5802/jolt.622

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