Hermitian geometry of Lie algebras with abelian ideals of codimension 2

We examine Hermitian metrics on unimodular Lie algebras which contains a J -invariant abelian ideal of codimension two, and give a classification for all Bismut Kähler-like and all Bismut torsion-parallel metrics on such Lie algebras.

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Bibliographic Details
Published in:Mathematische Zeitschrift 2023-07, Vol.304 (3), Article 51
Main Authors: Guo, Yuqin, Zheng, Fangyang
Format: Article
Language:English
Subjects:
Algebra
Lie groups
Mathematics
Mathematics and Statistics
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Description
Summary:We examine Hermitian metrics on unimodular Lie algebras which contains a J -invariant abelian ideal of codimension two, and give a classification for all Bismut Kähler-like and all Bismut torsion-parallel metrics on such Lie algebras.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-023-03315-5