Orthogonal separation of variables for spaces of constant curvature

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 the Stäckel matrices.

28 pages, one figure. Comments are welcome

References in corpus (9)

• Natural coordinates for a class of Benenti systems
• Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures
• Applications of Nijenhuis Geometry IV: multicomponent KdV and Camassa-Holm equations
• Complex variables for separation of Hamilton-Jacobi equation on real pseudo-Riemannian manifolds
• Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature
• Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation
• Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
• When a $(1,1)$-tensor generates separation of variables of a certain metric
• Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces

Cited by in corpus (2)

• On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
• Self-adjoint quantization of Stäckel integrable systems