Special Hermitian metrics and Lie groups

Abstract

A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form $\omega$ is $\partial \bar{\partial }$-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.

12 pages, to appear on the DGA2010 Proceedings

References in corpus (6)

• Twistor spaces for HKT manifolds
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• Formality in generalized Kahler geometry
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Cited by in corpus (3)

• Hermitian Curvature flow on unimodular Lie groups and static invariant metrics
• Almost Kähler structures on four dimensional unimodular Lie algebras
• Static SKT metrics on Lie groups