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Title: 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 metrics, have an intrinsic characterization which can be used to obtain them on a given space. 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.

Authors:
;  [1]
  1. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
Publication Date:
OSTI Identifier:
22306029
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSIFICATION; COORDINATES; DE SITTER SPACE; HAMILTON-JACOBI EQUATIONS; METRICS; RIEMANN SPACE; TENSORS

Citation Formats

Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca, and McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca. Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature. United States: N. p., 2014. Web. doi:10.1063/1.4893335.
Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca, & McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca. Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature. United States. doi:10.1063/1.4893335.
Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca, and McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca. Fri . "Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature". United States. doi:10.1063/1.4893335.
@article{osti_22306029,
title = {Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature},
author = {Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca and McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca},
abstractNote = {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 metrics, have an intrinsic characterization which can be used to obtain them on a given space. 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.},
doi = {10.1063/1.4893335},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 55,
place = {United States},
year = {Fri Aug 15 00:00:00 EDT 2014},
month = {Fri Aug 15 00:00:00 EDT 2014}
}