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arXiv · 2609.26191

Curvature property on Hermitian Lie algebras with abelian ideals of codimension two

Shuwen Chen·Fangyang Zheng
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Abstract

Let $(\mathfrak g,J,g)$ be a unimodular Hermitian Lie algebra containing an abelian ideal $\mathfrak a$ of real codimension two. We study the curvature behaviour of $g$ and show that, if $g$ has constant Chern holomorphic sectional curvature, then it must be Chern flat. We also show that, for every canonical metric connection $D_s^r$ of $g$ other than the Chern connection, if $D_s^r$ has constant holomorphic sectional curvature, then $g$ is Kähler flat, and in this case $\mathfrak g/\mathfrak a$ is abelian.

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Shuwen Chen, Fangyang Zheng. 2026-08-10. Curvature property on Hermitian Lie algebras with abelian ideals of codimension two. https://arxiv.org/abs/2609.26191

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