We study Killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the Hamilton-Jacobi equation. This work is motivated primarily by the case of spaces of constant curvature where warped products are abundant. We first characterize Killing tensors which have a natural algebraic decomposition in warped products. We then apply this result to show how one can obtain the Killing-Stackel space (KS-space) for separable coordinate systems decomposable in warped products. This result in combination with Benenti's theory for constructing the KS-space of certain special separable coordinates can be used to obtain the KS-space for all orthogonal separable coordinates found by Kalnins and Miller in Riemannian spaces of constant curvature. Next we characterize when a natural Hamiltonian is separable in coordinates decomposable in a warped product by showing that the conditions originally given by Benenti can be reduced. Finally we use this characterization and concircular tensors (a special type of torsionless conformal Killing tensor) to develop a general algorithm to determine when a natural Hamiltonian is separable in a special class of separable coordinates which include all orthogonal separable coordinates in spaces of constant curvature.
Symplectic mechanics of relativistic spinning compact bodies. I. linear-in-spin integrability under Killing-Yano symmetry
Université de Caen Normandie, ENSICAEN, CNRS/IN2P3, LPC Caen UMR6534（法国卡昂诺曼底大学、ENSICAEN、CNRS/IN2P3、LPC Caen UMR6534）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces
Stäckel problem for non-diagonal Killing tensors: Yano-Patterson lifts, algebra of strong symmetries and quadratic in momenta integrals
School of Mathematics, Loughborough University（拉夫堡大学数学学院）；Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan（哈萨克斯坦阿拉木图数学与数学建模研究所）；Faculty of Mechanics and Mathematics and Center for Fundamental and Applied Mathematics, Moscow State University（莫斯科国立大学力学与数学系及基础与应用数学中心）
