Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
Given a n-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of m ≤ n Killing two-tensors. Moreover, from the analysis of the eigenvalues, informat...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2007 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2007
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147786 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds / C. Chanu, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653935717711872 |
|---|---|
| author | Chanu, C. Rastelli, G. |
| author_facet | Chanu, C. Rastelli, G. |
| citation_txt | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds / C. Chanu, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a n-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of m ≤ n Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided.
|
| first_indexed | 2025-12-01T23:49:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147786 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:49:33Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chanu, C. Rastelli, G. 2019-02-16T08:09:39Z 2019-02-16T08:09:39Z 2007 Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds / C. Chanu, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70H20; 70G45 https://nasplib.isofts.kiev.ua/handle/123456789/147786 Given a n-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of m ≤ n Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. This research is partially supported by MIUR (National Research Project “Geometry of Dynamical System”) and by the research project “Progetto Lagrange” of Fondazione CRT. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds Article published earlier |
| spellingShingle | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds Chanu, C. Rastelli, G. |
| title | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_full | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_fullStr | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_full_unstemmed | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_short | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_sort | eigenvalues of killing tensors and separable webs on riemannian and pseudo-riemannian manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147786 |
| work_keys_str_mv | AT chanuc eigenvaluesofkillingtensorsandseparablewebsonriemannianandpseudoriemannianmanifolds AT rastellig eigenvaluesofkillingtensorsandseparablewebsonriemannianandpseudoriemannianmanifolds |