The Variety of Integrable Killing Tensors on the 3-Sphere
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Variety of Integrable Killing Tensors on the 3-Sphere
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| Creator |
Schöbel, K.
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| Description |
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.
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| Date |
2019-02-10T09:46:06Z
2019-02-10T09:46:06Z 2014 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 53A60; 14H10; 14M12 DOI:10.3842/SIGMA.2014.080 http://dspace.nbuv.gov.ua/handle/123456789/146598 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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