Are Orthogonal Separable Coordinates Really Classified?
We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new, algebraic geometric approach to the classification of orthogonal...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147741 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862663426728263680 |
|---|---|
| author | Schöbel, K. |
| author_facet | Schöbel, K. |
| citation_txt | Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new, algebraic geometric approach to the classification of orthogonal separable coordinates by studying the structure of this variety. We give an example where this approach reveals unexpected structure in the well known classification and pose a number of problems arising naturally in this context.
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| first_indexed | 2025-12-07T15:11:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147741 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:11:51Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schöbel, K. 2019-02-15T18:59:16Z 2019-02-15T18:59:16Z 2016 Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H70; 53A60; 58D27 DOI:10.3842/SIGMA.2016.041 https://nasplib.isofts.kiev.ua/handle/123456789/147741 We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new, algebraic geometric approach to the classification of orthogonal separable coordinates by studying the structure of this variety. We give an example where this approach reveals unexpected structure in the well known classification and pose a number of problems arising naturally in this context. 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.
 This notice is based on a talk held at the workshop “Analytical Mechanics and Dif ferential
 Geometry” at the Universit`a di Torino on 12th and 13th March 2015 on the occasion of Sergio
 Benenti’s 70th birthday. The author would like to thank the organisers, Claudia Chanu and
 Giovanni Rastelli, for their kind invitation and hospitality, as well as Willard Miller for valuable
 discussions on the subject. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Are Orthogonal Separable Coordinates Really Classified? Article published earlier |
| spellingShingle | Are Orthogonal Separable Coordinates Really Classified? Schöbel, K. |
| title | Are Orthogonal Separable Coordinates Really Classified? |
| title_full | Are Orthogonal Separable Coordinates Really Classified? |
| title_fullStr | Are Orthogonal Separable Coordinates Really Classified? |
| title_full_unstemmed | Are Orthogonal Separable Coordinates Really Classified? |
| title_short | Are Orthogonal Separable Coordinates Really Classified? |
| title_sort | are orthogonal separable coordinates really classified? |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147741 |
| work_keys_str_mv | AT schobelk areorthogonalseparablecoordinatesreallyclassified |