Are Orthogonal Separable Coordinates Really Classified?

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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dc.contributor.author	Schöbel, K.
dc.date.accessioned	2019-02-15T18:59:16Z
dc.date.available	2019-02-15T18:59:16Z
dc.date.issued	2016
dc.identifier.citation	Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 14H70; 53A60; 58D27
dc.identifier.other	DOI:10.3842/SIGMA.2016.041
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147741
dc.description.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.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html. This notice is based on a talk held at the workshop “Analytical Mechanics and Dif ferential Geometry” at the Universit`a di Torino on 12th and 13th March 2015 on the occasion of Sergio Benenti’s 70th birthday. The author would like to thank the organisers, Claudia Chanu and Giovanni Rastelli, for their kind invitation and hospitality, as well as Willard Miller for valuable discussions on the subject.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Are Orthogonal Separable Coordinates Really Classified?	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA