Area formula for spherical polygons via prequantization

Publication

SIAM Journal on Applied Algebra and Geometry (SIAGA)

Abstract

We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss–Bonnet theorem that requires measuring angles, the new formula mimics Green’s theorem and is applicable to a wider range of degenerate spherical curves and polygons.

Resources

• Paper (9.8 MB)

Citation

@article{ChernIshida2024,
  author = {Chern, Albert and Ishida, Sadashige},
  title = {Area Formula for Spherical Polygons via Prequantization},
  journal = {SIAM Journal on Applied Algebra and Geometry},
  volume = {8},
  number = {3},
  pages = {782-796},
  year = {2024},
  doi = {10.1137/23M1565255},
  URL = {https://doi.org/10.1137/23M1565255},
  eprint = {https://doi.org/10.1137/23M1565255},
  abstract = {We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss–Bonnet theorem that requires measuring angles, the new formula mimics Green’s theorem and is applicable to a wider range of degenerate spherical curves and polygons.}
}

Acknowledgements

The authors acknowledge anonymous referees for their reviews and insightful suggestions, and Chris Wojtan for his continuous support through discussions. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA) and the National Science Foundation CAREER Award 2239062.