Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature

Abstract

We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the diagonal curvature condition. The metrics we find either correspond to a Benenti system or are warped product metrics where the induced metric on the base manifold corresponds to a Benenti system. Furthermore we show that most metrics we find are characterized by concircular tensors; these metrics, called Kalnins-Eisenhart-Miller (KEM) metrics, have an intrinsic characterization which can be used to obtain them. In conjunction with other results, we show that the metrics we found constitute all separable metrics for Riemannian spaces of constant curvature and de Sitter space.

References in corpus (2)

• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation

Cited by in corpus (3)

• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces