The Variety of Integrable Killing Tensors on the 3-Sphere
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...
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2014
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146598 |
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| Zitieren: | 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. |
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irk-123456789-1465982019-02-11T01:23:42Z The Variety of Integrable Killing Tensors on the 3-Sphere Schöbel, K. 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. 2014 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Schöbel, K. |
| spellingShingle |
Schöbel, K. The Variety of Integrable Killing Tensors on the 3-Sphere Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schöbel, K. |
| author_sort |
Schöbel, K. |
| title |
The Variety of Integrable Killing Tensors on the 3-Sphere |
| title_short |
The Variety of Integrable Killing Tensors on the 3-Sphere |
| title_full |
The Variety of Integrable Killing Tensors on the 3-Sphere |
| title_fullStr |
The Variety of Integrable Killing Tensors on the 3-Sphere |
| title_full_unstemmed |
The Variety of Integrable Killing Tensors on the 3-Sphere |
| title_sort |
variety of integrable killing tensors on the 3-sphere |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146598 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT schobelk thevarietyofintegrablekillingtensorsonthe3sphere AT schobelk varietyofintegrablekillingtensorsonthe3sphere |
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2025-07-11T00:18:11Z |
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2025-07-11T00:18:11Z |
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