Concircular tensors in Spaces of Constant Curvature: With Applications to Orthogonal Separation of The Hamilton-Jacobi Equation

摘要

We study concircular tensors in spaces of constant curvature and then applythe results obtained to the problem of the orthogonal separation of theHamilton-Jacobi equation on these spaces. Any coordinates which separate thegeodesic Hamilton-Jacobi equation are called separable. Specifically for spacesof constant curvature, we obtain canonical forms of concircular tensors modulothe action of the isometry group, we obtain the separable coordinates inducedby irreducible concircular tensors, and we obtain warped products adapted toreducible concircular tensors. Using these results, we show how to enumeratethe isometrically inequivalent orthogonal separable coordinates, construct thetransformation from separable to Cartesian coordinates, and execute theBenenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separatingnatural Hamilton-Jacobi equations.