Eigenvalues of Killing Tensors and Separable Webs on Riemannian and PseudoRiemannian Manifolds
Abstract
Given a ndimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic HamiltonJacobi equation by means of the eigenvalues of m ≤ n Killing twotensors. 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 nonorthogonal 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 Lsystems is provided.
 Publication:

SIGMA
 Pub Date:
 February 2007
 DOI:
 10.3842/SIGMA.2007.021
 arXiv:
 arXiv:nlin/0612042
 Bibcode:
 2007SIGMA...3..021C
 Keywords:

 variable separation;
 HamiltonJacobi equation;
 Killing tensors;
 (pseudo)Riemannian manifolds;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/