Locally conformally Kähler structures on unimodular Lie groups

ADRIÁN ANDRADA; MARCOS ORIGLIA

GEOMETRIAE DEDICATA

SPRINGER

Lugar: Berlin; Año: 2015 vol. 179 p. 197 - 216

0046-5755

We study left-invariant locally conformally K ̈ahler 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.