Locally conformally Kähler structures on four-dimensional solvable Lie algebras

Daniele Angella; Marcos Origlia

doi:10.1515/coma-2020-0001

Locally conformally Kähler structures on four-dimensional solvable Lie algebras

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Abstract

We classify and investigate locally conformally Kähler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the 4-dimensional structures in our classification.

Original language	English
Number of pages	35
Journal	Complex Manifolds
Volume	7
Issue number	1
DOIs	https://doi.org/10.1515/coma-2020-0001
Publication status	Published - Jan 2020
Externally published	Yes

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Cite this

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abstract = "We classify and investigate locally conformally K{\"a}hler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the 4-dimensional structures in our classification.",

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AB - We classify and investigate locally conformally Kähler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the 4-dimensional structures in our classification.

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