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PreprintarXiv licencearXiv

Delambre--Gauss Formulas in Complex Hyperbolic Space

  • Jiming Ma
  • Baohua Xie
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Abstract

We establish a Delambre--Gauss matrix identity for oriented right-angled hexagons in the complex hyperbolic plane. The six complex length parameters of a hexagon determine two alternating 3×3 matrices whose product is central in (\mathrm{SU}(2,1)\). The resulting nine entry-wise equations extend the Delambre-Gauss formula of Tan, Wong, and Zhang in 4-dimensional hyperbolic geometry to this complex hyperbolic setting.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026delambregauss,
  title = {{Delambre--Gauss Formulas in Complex Hyperbolic Space}},
  author = {Jiming Ma and Baohua Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33468},
  eprint = {2610.33468},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33468},
}
RIS
TY  - UNPB
TI  - Delambre--Gauss Formulas in Complex Hyperbolic Space
AU  - Jiming Ma
AU  - Baohua Xie
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33468
UR  - https://arxiv.org/abs/2610.33468
AB  - We establish a Delambre--Gauss matrix identity for oriented right-angled hexagons in the complex hyperbolic plane. The six complex length parameters of a hexagon determine two alternating 3×3 matrices whose product is central in (\mathrm{SU}(2,1)\). The resulting nine entry-wise equations extend the Delambre-Gauss formula of Tan, Wong, and Zhang in 4-dimensional hyperbolic geometry to this complex hyperbolic setting.
ER  -