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The Variety of Integrable Killing Tensors on the 3-Sphere
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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The Variety of Integrable Killing Tensors on the 3-Sphere
Інший ID:
2010 Mathematics Subject Classification: 53A60; 14H10; 14M12
DOI:10.3842/SIGMA.2014.080
DOI:10.3842/SIGMA.2014.080
Посилання:
The Variety of Integrable Killing Tensors on the 3-Sphere / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 46 назв. — англ.
Підтримка:
I would like to express my gratitude to Robert Milson for his motivation and the inspiring
discussions about my findings. I would also like to thank Alexander P. Veselov for pointing out
the link between my solution and moduli spaces of stable curves. Finally, I would like to thank
the anonymous referees, who helped to improve the paper considerably with their comments
and additional references.
Дата:
2014
Переглядів:
510
Завантажень:
181
Анотація:
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing tensors on the sphere S³ and give a set of isometry invariants for the integrability of a Killing tensor. We describe explicitly the space of solutions as well as its quotient under isometries as projective varieties and interpret their algebro-geometric properties in terms of Killing tensors. Furthermore, we identify all Stäckel systems in these varieties. This allows us to recover the known list of separation coordinates on S³ in a simple and purely algebraic way. In particular, we prove that their moduli space is homeomorphic to the associahedron K₄.
