2011/04/08 by Enrietti, Nicola, Fino, Anna
#32J27 #53C30 #53C55 #53D05 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1104.1612
A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form ω is ∂ ∂-closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a 2n-dimensional SKT Lie algebra \mathfrak g and using a Hermitian flat connection on \mathfrak g we construct a 4n-dimensional SKT Lie algebra. We apply this method to some 4-dimensional SKT Lie algebras. Moreover, we classify symplectic forms taming complex structures on 4-dimensional Lie algebras.