Equivalence problem for the orthogonal webs on the sphere
Abstract
We solve the equivalence problem for the orthogonally separable webs on the three-sphere under the action of the isometry group. This continues a classical project initiated by Olevsky in which he solved the corresponding canonical forms problem. The solution to the equivalence problem together with the results by Olevsky forms a complete solution to the problem of orthogonal separation of variables to the Hamilton-Jacobi equation defined on the three-sphere via orthogonal separation of variables. It is based on invariant properties of the characteristic Killing two-tensors in addition to properties of the corresponding algebraic curvature tensor and the associated Ricci tensor. The result is illustrated by a non-trivial application to a natural Hamiltonian defined on the three-sphere.
Cite
@article{arxiv.1009.4244,
title = {Equivalence problem for the orthogonal webs on the sphere},
author = {Caroline Cochran and Raymond G. McLenaghan and Roman G. Smirnov},
journal= {arXiv preprint arXiv:1009.4244},
year = {2015}
}
Comments
32 pages