Locally conformally Kähler structures on unimodular Lie groups

A. Andrada; M. Origlia

doi:10.1007/s10711-015-0076-6

Locally conformally Kähler structures on unimodular Lie groups

A. Andrada, M. Origlia

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	197-216
Number of pages	20
Journal	Geometriae Dedicata
Volume	179
Issue number	1
DOIs	https://doi.org/10.1007/s10711-015-0076-6
Publication status	Published - 1 Dec 2015
Externally published	Yes

Keywords

Abelian complex structure
Hermitian metric
Locally conformally Kähler metric

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Locally conformally Kähler structures on unimodular Lie groups

Abstract

Keywords

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