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

Chanu, C., Rastelli, G. (2007). Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 3(3) [10.3842/SIGMA.2007.021].

Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds

CHANU, CLAUDIA MARIA;
2007

Abstract

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
Articolo in rivista - Articolo scientifico
Variable separation; Riemannian geometry
English
2007
3
3
021
none
Chanu, C., Rastelli, G. (2007). Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 3(3) [10.3842/SIGMA.2007.021].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/9947
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