Locally conformally balanced metrics on almost abelian Lie algebras

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 ba...

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Autor principal:	Paradiso Fabio
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	almost abelian lie algebras hermitian metrics locally conformally balanced locally conformally kähler hyperkähler locally conformally hyperkähler 53c15 53c30 53c55 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0bd8b35ff21c4e359dce6eb086017d66
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spelling	oai:doaj.org-article:0bd8b35ff21c4e359dce6eb086017d662021-12-05T14:10:45ZLocally conformally balanced metrics on almost abelian Lie algebras2300-744310.1515/coma-2020-0111https://doaj.org/article/0bd8b35ff21c4e359dce6eb086017d662021-07-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0111https://doaj.org/toc/2300-7443We 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.Paradiso FabioDe Gruyterarticlealmost abelian lie algebrashermitian metricslocally conformally balancedlocally conformally kählerhyperkählerlocally conformally hyperkähler53c1553c3053c55MathematicsQA1-939ENComplex Manifolds, Vol 8, Iss 1, Pp 196-207 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	almost abelian lie algebras hermitian metrics locally conformally balanced locally conformally kähler hyperkähler locally conformally hyperkähler 53c15 53c30 53c55 Mathematics QA1-939
spellingShingle	almost abelian lie algebras hermitian metrics locally conformally balanced locally conformally kähler hyperkähler locally conformally hyperkähler 53c15 53c30 53c55 Mathematics QA1-939 Paradiso Fabio Locally conformally balanced metrics on almost abelian Lie algebras
description	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.
format	article
author	Paradiso Fabio
author_facet	Paradiso Fabio
author_sort	Paradiso Fabio
title	Locally conformally balanced metrics on almost abelian Lie algebras
title_short	Locally conformally balanced metrics on almost abelian Lie algebras
title_full	Locally conformally balanced metrics on almost abelian Lie algebras
title_fullStr	Locally conformally balanced metrics on almost abelian Lie algebras
title_full_unstemmed	Locally conformally balanced metrics on almost abelian Lie algebras
title_sort	locally conformally balanced metrics on almost abelian lie algebras
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/0bd8b35ff21c4e359dce6eb086017d66
work_keys_str_mv	AT paradisofabio locallyconformallybalancedmetricsonalmostabelianliealgebras
_version_	1718371775443632128

Locally conformally balanced metrics on almost abelian Lie algebras

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