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PreprintCC BY 4.0arXiv

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

  • Shuwen Chen
  • Fangyang Zheng
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Abstract

Let (g,J,g) be a unimodular Hermitian Lie algebra containing an abelian ideal 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 Dsr of g other than the Chern connection, if Dsr has constant holomorphic sectional curvature, then g is Kähler flat, and in this case g/a is abelian.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026curvature,
  title = {{Curvature property on Hermitian Lie algebras with abelian ideals of codimension two}},
  author = {Shuwen Chen and Fangyang Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26191},
  eprint = {2609.26191},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26191},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Curvature property on Hermitian Lie algebras with abelian ideals of codimension two
AU  - Shuwen Chen
AU  - Fangyang Zheng
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.26191
UR  - https://arxiv.org/abs/2609.26191
AB  - Let (g,J,g) be a unimodular Hermitian Lie algebra containing an abelian ideal 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 g/a is abelian.
ER  -