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PreprintCC BY 4.0arXiv

Constant Chern holomorphic sectional curvature on two-step solvmanifolds

  • Shanlin Guan
  • Yuqin Guo
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Abstract

Let M=Γbackslash G be a compact solvmanifold with a left-invariant Hermitian structure whose Lie algebra is two-step solvable. If the Chern holomorphic sectional curvature is constant, then the derived algebra is J-invariant and the Chern connection is flat. At the Lie-algebra level, we also prove that constant Chern holomorphic sectional curvature is impossible for a unimodular two-step solvable Hermitian Lie algebra of mixed Freibert-Swann type.

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Cite

BibTeXRIS
BibTeX
@misc{guan2026constant,
  title = {{Constant Chern holomorphic sectional curvature on two-step solvmanifolds}},
  author = {Shanlin Guan and Yuqin Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34820},
  eprint = {2610.34820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34820},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Constant Chern holomorphic sectional curvature on two-step solvmanifolds
AU  - Shanlin Guan
AU  - Yuqin Guo
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34820
UR  - https://arxiv.org/abs/2610.34820
AB  - Let M=Γbackslash G be a compact solvmanifold with a left-invariant Hermitian structure whose Lie algebra is two-step solvable. If the Chern holomorphic sectional curvature is constant, then the derived algebra is J-invariant and the Chern connection is flat. At the Lie-algebra level, we also prove that constant Chern holomorphic sectional curvature is impossible for a unimodular two-step solvable Hermitian Lie algebra of mixed Freibert-Swann type.
ER  -