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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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Are Orthogonal Separable Coordinates Really Classified?
Інший ID:
2010 Mathematics Subject Classification: 14H70; 53A60; 58D27
DOI:10.3842/SIGMA.2016.041
DOI:10.3842/SIGMA.2016.041
Посилання:
Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ.
Підтримка:
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.
Дата:
2016
Переглядів:
557
Завантажень:
176
Анотація:
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.
