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arXiv · 1009.4244

Equivalence problem for the orthogonal webs on the sphere

Caroline Cochran·Raymond G. McLenaghan·Roman G. Smirnov
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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.

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Caroline Cochran, Raymond G. McLenaghan, Roman G. Smirnov. 2010-09-22. Equivalence problem for the orthogonal webs on the sphere. https://doi.org/10.1063/1.3578773

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