Geodesic
Nijenhuis Integrability for Killing Tensors
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Konrad Sch\"obel},
     title = {Nijenhuis {Integrability} for {Killing} {Tensors}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2016},
     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a23/}
}
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Konrad Schöbel. Nijenhuis Integrability for Killing Tensors. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a23/

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