Geometriae Dedicata

, Volume 179, Issue 1, pp 197–216 | Cite as

Locally conformally Kähler structures on unimodular Lie groups

Original paper


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 \(\mathbb {R}\) and a Heisenberg Lie algebra.


Hermitian metric Locally conformally Kähler metric  Abelian complex structure 

Mathematics Subject Classification (2010)

53C15 53B35 53C30 



The authors would like to thank L. Ornea and I. Dotti for useful comments and the referee for his/her thorough review of the manuscript and the constructive comments. The authors were partially supported by CONICET, ANPCyT and SECyT-UNC (Argentina).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.FaMAF-CIEMUniversidad Nacional de CórdobaCórdobaArgentina

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