Are Orthogonal Separable Coordinates Really Classified?

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Author: Schöbel, K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147741
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ.

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...