Complex Manifolds (Jul 2021)

Locally conformally balanced metrics on almost abelian Lie algebras

  • Paradiso Fabio

DOI
https://doi.org/10.1515/coma-2020-0111
Journal volume & issue
Vol. 8, no. 1
pp. 196 – 207

Abstract

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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.

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