Invariant strong KT geometry on four-dimensional solvable lie groups

Thomas Bruun Madsen, Andrew Swann

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9 Citations (Scopus)


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.

Original languageEnglish
JournalJournal of Lie Theory
Pages (from-to)55-70
Number of pages16
Publication statusPublished - 10 Jan 2011
Externally publishedYes


  • Complex structure
  • Hermitian metric
  • Kähler with torsion
  • Solvable Lie group
  • Strong KT geometry


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