Nijenhuis Integrability for Killing Tensors
Differential Geometry
2016-03-08 v2 Dynamical Systems
Abstract
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for a Killing tensor the third and most complicated of these equations is redundant. This considerably simplifies the classification of orthogonal separation coordinates on arbitrary (pseudo-)Riemannian manifolds.
Cite
@article{arxiv.1502.07516,
title = {Nijenhuis Integrability for Killing Tensors},
author = {Konrad Schöbel},
journal= {arXiv preprint arXiv:1502.07516},
year = {2016}
}