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Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
Інший ID:
2000 Mathematics Subject Classification: 70H20; 70G45
Посилання:
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.
Підтримка:
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.
Дата:
2007
Переглядів:
491
Завантажень:
237
Анотація:
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.
