Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chen, Shuwen, Zheng, Fangyang
Institution: Chongqing Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214066659