Locally conformally Kähler structures on unimodular Lie groups

A. Andrada, M. Origlia

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We study left-invariant locally conformally Kähler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is bi-invariant or abelian. In the former case, we show that no such Lie algebra is unimodular, while in the latter, we prove that if the Lie algebra is unimodular, then it is isomorphic to the product of R and a Heisenberg Lie algebra.

Original languageEnglish
Pages (from-to)197-216
Number of pages20
JournalGeometriae Dedicata
Issue number1
Publication statusPublished - 1 Dec 2015
Externally publishedYes


  • Abelian complex structure
  • Hermitian metric
  • Locally conformally Kähler metric

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