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This article is cited in 4 scientific papers (total in 4 papers)
Are Orthogonal Separable Coordinates Really Classified?
Konrad Schöbel Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany
Abstract:
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.
Received: October 30, 2015; in final form March 15, 2016; Published online April 26, 2016
Citation:
Konrad Schöbel, “Are Orthogonal Separable Coordinates Really Classified?”, SIGMA, 12 (2016), 041, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1123 https://www.mathnet.ru/eng/sigma/v12/p41
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