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: Schöbel, K.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2016
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147721
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Nijenhuis Integrability for Killing Tensors
spellingShingle Nijenhuis Integrability for Killing Tensors
Schöbel, K.
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
author Schöbel, K.
author_facet Schöbel, K.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT schobelk nijenhuisintegrabilityforkillingtensors
first_indexed 2025-12-07T15:27:44Z
last_indexed 2025-12-07T15:27:44Z
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