Area formula for spherical polygons via prequantization
Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv, 2303.14555.
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Author
Chern, Albert;
Ishida, SadashigeISTA
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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.
Publishing Year
Date Published
2023-03-25
Journal Title
arXiv
Acknowledgement
The authors acknowledge Chris Wojtan for his continuous support to the present work through discussions and advice. 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).
Article Number
2303.14555
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Cite this
Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv. doi:10.48550/arXiv.2303.14555
Chern, A., & Ishida, S. (n.d.). Area formula for spherical polygons via prequantization. arXiv. https://doi.org/10.48550/arXiv.2303.14555
Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2303.14555.
A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” arXiv. .
Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv, 2303.14555.
Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” ArXiv, 2303.14555, doi:10.48550/arXiv.2303.14555.
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