Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space
We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separabl...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211526 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862668549658509312 |
|---|---|
| author | Valero, Carlos McLenaghan, Raymond G. |
| author_facet | Valero, Carlos McLenaghan, Raymond G. |
| citation_txt | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separable webs modulo the action of the isometry group. The eighty-eight inequivalent coordinate charts adapted to the webs are also determined and listed. We find a number of separable webs that do not appear in previous works in the literature. Further, the method used seems to be more efficient and concise than those employed in earlier works.
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| first_indexed | 2026-03-16T12:21:30Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211526 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T12:21:30Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Valero, Carlos McLenaghan, Raymond G. 2026-01-05T12:25:23Z 2022 Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space. Carlos Valero and Raymond G. Mclenaghan. SIGMA 18 (2022), 019, 28 pages 1815-0659 2020 Mathematics Subject Classification: 53Z05; 70H20; 83A05 arXiv:1805.12228 https://nasplib.isofts.kiev.ua/handle/123456789/211526 https://doi.org/10.3842/SIGMA.2022.019 We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separable webs modulo the action of the isometry group. The eighty-eight inequivalent coordinate charts adapted to the webs are also determined and listed. We find a number of separable webs that do not appear in previous works in the literature. Further, the method used seems to be more efficient and concise than those employed in earlier works. The authors wish to thank K. Rajaratnam and the anonymous referees for their careful reading of the paper and a number of helpful suggestions and comments. We also wish to acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada in the form of an Undergraduate Student Research Award (CV) and a Discovery Grant (RGM). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space Article published earlier |
| spellingShingle | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space Valero, Carlos McLenaghan, Raymond G. |
| title | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space |
| title_full | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space |
| title_fullStr | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space |
| title_full_unstemmed | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space |
| title_short | Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space |
| title_sort | classification of the orthogonal separable webs for the hamilton-jacobi and klein-gordon equations on 3-dimensional minkowski space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211526 |
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