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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147741 |
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| Цитувати: | Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147741 |
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irk-123456789-1477412019-02-16T01:24:56Z Are Orthogonal Separable Coordinates Really Classified? Schöbel, K. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147741 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Schöbel, K. |
| spellingShingle |
Schöbel, K. Are Orthogonal Separable Coordinates Really Classified? Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Schöbel, K. |
| author_sort |
Schöbel, K. |
| title |
Are Orthogonal Separable Coordinates Really Classified? |
| title_short |
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_sort |
are orthogonal separable coordinates really classified? |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147741 |
| citation_txt |
Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:11Z |
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2023-05-20T17:28:11Z |
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