Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces

Abstract

We review the theory of orthogonal separation of variables on pseudo-Riemannian manifolds of constant non-zero curvature via concircular tensors and warped products. We then apply this theory simultaneously to both the three-dimensional Hyperbolic and de Sitter spaces, obtaining an invariant classification of the thirty-four orthogonal separable webs on each space, modulo action of the respective isometry groups. The inequivalent coordinate charts adapted to each web are also determined and listed. The results obtained for Hyperbolic 3-space agree with those in the literature, while the results for de Sitter 3-space appear to be new.

References in corpus (4)

• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature
• Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation
• Equivalence problem for the orthogonal webs on the sphere

Cited by in corpus (1)

• Orthogonal separation of variables for spaces of constant curvature