Geodesic
Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $m\leq n$ 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.
Keywords: variable separation; Hamilton–Jacobi equation; Killing tensors; (pseudo-) Riemannian manifolds. 
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     title = {Eigenvalues of {Killing} {Tensors} and {Separable} {Webs} on {Riemannian} and {Pseudo-Riemannian} {Manifolds}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a20/}
}
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Claudia Chanu; Giovanni Rastelli. Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a20/

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