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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147721 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Nijenhuis Integrability for Killing Tensors / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862669438432575488 |
|---|---|
| author | Schöbel, K. |
| author_facet | Schöbel, K. |
| citation_txt | Nijenhuis Integrability for Killing Tensors / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:27:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147721 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:27:44Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schöbel, K. 2019-02-15T18:42:06Z 2019-02-15T18:42:06Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147721 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. This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
 of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
 The author would like to acknowledge the anonymous referees for their contribution to improve
 the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nijenhuis Integrability for Killing Tensors Article published earlier |
| spellingShingle | Nijenhuis Integrability for Killing Tensors Schöbel, K. |
| title | 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_short | Nijenhuis Integrability for Killing Tensors |
| title_sort | nijenhuis integrability for killing tensors |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147721 |
| work_keys_str_mv | AT schobelk nijenhuisintegrabilityforkillingtensors |