Are Orthogonal Separable Coordinates Really Classified?

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...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2016
Автор: Schöbel, K.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2016
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/147741
Теги: Додати тег
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Are Orthogonal Separable Coordinates Really Classified? / K. Schöbel // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме: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.