Area formula for spherical polygons via prequantization
Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.
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Author
Chern, Albert;
Ishida, SadashigeISTA
Corresponding author has ISTA affiliation
Department
Grant
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
2024-09-23
Journal Title
SIAM Journal on Applied Algebra and Geometry
Publisher
Society for Industrial and Applied Mathematics
Acknowledgement
This work was funded by European Research Council Consolidator grant 101045083 CoDiNA and National Science Foundation CAREER award 2239062. Some figures in the article were generated by the software Houdini and its education license was provided by SideFX. 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.
Volume
8
Issue
3
Page
782-796
eISSN
IST-REx-ID
Cite this
Chern A, Ishida S. Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. 2024;8(3):782-796. doi:10.1137/23M1565255
Chern, A., & Ishida, S. (2024). Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1565255
Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” SIAM Journal on Applied Algebra and Geometry. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1565255.
A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” SIAM Journal on Applied Algebra and Geometry, vol. 8, no. 3. Society for Industrial and Applied Mathematics, pp. 782–796, 2024.
Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization. SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.
Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” SIAM Journal on Applied Algebra and Geometry, vol. 8, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 782–96, doi:10.1137/23M1565255.
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