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:Англійська
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
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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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publisher Інститут математики НАН України
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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