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Nijenhuis Integrability for Killing Tensors
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three no...
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Інститут математики НАН України
2016
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147721 |
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irk-123456789-1477212019-02-16T01:24:06Z Nijenhuis Integrability for Killing Tensors Schöbel, K. The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for a Killing tensor the third and most complicated of these equations is redundant. This considerably simplifies the classification of orthogonal separation coordinates on arbitrary (pseudo-)Riemannian manifolds. 2016 Article Nijenhuis Integrability for Killing Tensors / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70H06; 53A60; 53B20 DOI:10.3842/SIGMA.2016.024 http://dspace.nbuv.gov.ua/handle/123456789/147721 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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English |
| description |
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for a Killing tensor the third and most complicated of these equations is redundant. This considerably simplifies the classification of orthogonal separation coordinates on arbitrary (pseudo-)Riemannian manifolds. |
| format |
Article |
| author |
Schöbel, K. |
| spellingShingle |
Schöbel, K. Nijenhuis Integrability for Killing Tensors Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schöbel, K. |
| author_sort |
Schöbel, K. |
| title |
Nijenhuis Integrability for Killing Tensors |
| title_short |
Nijenhuis Integrability for Killing Tensors |
| title_full |
Nijenhuis Integrability for Killing Tensors |
| title_fullStr |
Nijenhuis Integrability for Killing Tensors |
| title_full_unstemmed |
Nijenhuis Integrability for Killing Tensors |
| title_sort |
nijenhuis integrability for killing tensors |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147721 |
| citation_txt |
Nijenhuis Integrability for Killing Tensors / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT schobelk nijenhuisintegrabilityforkillingtensors |
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2023-05-20T17:28:08Z |
| last_indexed |
2023-05-20T17:28:08Z |
| _version_ |
1796153362687721472 |