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Hermitian geometry of Lie algebras with abelian ideals of codimension 2

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Abstract

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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Acknowledgements

The second named author would like to thank Bo Yang and Quanting Zhao for their interests and/or helpful discussions.

Funding

Zheng is partially supported by National Natural Science Foundations of China with the Grant Nos. 12071050 and 12141101, Chongqing Grant cstc2021ycjh-bgzxm0139, and is supported by the 111 Project D21024.

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  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Yuqin Guo & Fangyang Zheng

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  1. Yuqin Guo
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Correspondence to Fangyang Zheng.

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Guo, Y., Zheng, F. Hermitian geometry of Lie algebras with abelian ideals of codimension 2. Math. Z. 304, 51 (2023). https://doi.org/10.1007/s00209-023-03315-5

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