Geodesic
Are Orthogonal Separable Coordinates Really Classified?
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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We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new, algebraic geometric approach to the classification of orthogonal separable coordinates by studying the structure of this variety. We give an example where this approach reveals unexpected structure in the well known classification and pose a number of problems arising naturally in this context.
Keywords: separation of variables; Stäckel systems; Deligne–Mumford moduli spaces; Stasheff polytopes; operads. 
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     author = {Konrad Sch\"obel},
     title = {Are {Orthogonal} {Separable} {Coordinates} {Really} {Classified?}},
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}
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Konrad Schöbel. Are Orthogonal Separable Coordinates Really Classified?. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a40/

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