Orthogonal separation of variables for spaces of constant curvature-Reference-Cited by-同舟云学术

Orthogonal separation of variables for spaces of constant curvature

Published:2024-02-20 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Bolsinov Alexey V.¹^ORCID,Konyaev Andrey Yu.²,Matveev Vladimir S.³^ORCID

Affiliation:

1. Department of Mathematical Sciences , [ 152008]Loughborough University, Loughborough LE11 3TU , United Kingdom

2. Faculty of Mechanics and Mathematics , [ 64935]Moscow State University; and Moscow Center for Fundamental and Applied Mathematics, 119992 , Moscow , Russia

3. Institut für Mathematik , [ 9378]Friedrich Schiller Universität Jena, 07737 Jena , Germany

Abstract

Abstract We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and Stäckel matrices.

Funder

Deutsche Forschungsgemeinschaft

Australian Research Council

Russian Science Foundation

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0300/pdf

Reference67 articles.

1. S. I. Alber, On stationary problems for equations of Korteweg–de Vries type, Comm. Pure Appl. Math. 34 (1981), no. 2, 259–272.

2. S. Bandyopadhyay, B. Dacorogna, V. S. Matveev and M. Troyanov, Bernhard Riemann 1861 revisited: Existence of flat coordinates for an arbitrary bilinear form, Math. Z. 305 (2023), no. 1, Paper No. 12.

3. E. Beltrami, Risoluzione del problema: Riportare i punti di una superficie sopra un piano in modo che le linee geodetiche vengano rappresentate da linee rette, Ann. Mat. 7 (1865), 185–204.

4. S. Benenti, Separability structures on Riemannian manifolds, Differential Geometrical Methods in Mathematical Physics (Aix-en-Provence/Salamanca 1979), Lecture Notes in Math. 836, Springer, Berlin (1980), 512–538.

5. S. Benenti, Inertia tensors and Stäckel systems in the Euclidean spaces, Rend. Semin. Mat. Univ. Padova 50 (1992), 315–341.