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arXiv · 1502.07516

Nijenhuis Integrability for Killing Tensors

Konrad Schöbel
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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.

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Konrad Schöbel. 2015-02-26. Nijenhuis Integrability for Killing Tensors. https://doi.org/10.3842/sigma.2016.024

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