Geodesic
Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups
Journal of Lie theory, Tome 21 (2011) no. 1, pp. 55-7

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 53C55, 53C30, 32M10
Mots-clés : Hermitian metric, complex structure, strong KT geometry, Kaehler with torsion, solvable Lie group 
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     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--7},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_1_JLT_2011_21_1_a1/}
}
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T. B. Madsen; A. Swann . Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups. Journal of Lie theory, Tome 21 (2011) no. 1, pp. 55-7. http://geodesic.mathdoc.fr/item/JLT_2011_21_1_JLT_2011_21_1_a1/