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

2014/04/10 by Krishan Rajaratnam, Rajaratnam, Krishan, R. G. McLenaghan +1
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Elasticity and Material Modeling #FOS: Physical sciences #Mathematical Physics (math-ph) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1404.2847

openalex publication_date 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic Hamilton-Jacobi equation are called separable. Specifically for spaces of constant curvature, we obtain canonical forms of concircular tensors modulo the action of the isometry group, we obtain the separable coordinates induced by irreducible concircular tensors, and we obtain warped products adapted to reducible concircular tensors. Using these results, we show how to enumerate the isometrically inequivalent orthogonal separable coordinates, construct the transformation from separable to Cartesian coordinates, and execute the Benenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separating natural Hamilton-Jacobi equations.

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