This article is cited in 1 paper

Nijenhuis Integrability for Killing Tensors

Konrad Schöbel

Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany

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.

Keywords: integrable systems; separation of variables; Killing tensors; Nijenhuis tensor; Haantjes tensor.

MSC: 70H06;53A60;53B20

Received: October 30, 2015; in final form February 26, 2016; Published online March 7, 2016

Language: English

DOI: 10.3842/SIGMA.2016.024

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ArXiv: 1502.07516