We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional almost abelian Lie algebras admitting locally conformally balanced metrics and study some compatibility results between different types of special Hermitian metrics on almost abelian Lie groups and their compact quotients. We end by classifying almost abelian Lie algebras admitting locally conformally hyperkähler structures.

Locally conformally balanced metrics on almost abelian Lie algebras

Paradiso F.
2021-01-01

Abstract

We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional almost abelian Lie algebras admitting locally conformally balanced metrics and study some compatibility results between different types of special Hermitian metrics on almost abelian Lie groups and their compact quotients. We end by classifying almost abelian Lie algebras admitting locally conformally hyperkähler structures.
2021
8
1
196
207
https://www.degruyter.com/document/doi/10.1515/coma-2020-0111/html
Almost abelian Lie algebras, Hermitian metrics, Hyperkähler, Locally conformally balanced, Locally conformally hyperkähler, Locally conformally Kähler
Paradiso F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1866802
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