Gravitational Instantons, Confocal Quadrics and Separability of the Schrödinger and Hamilton-Jacobi equations
arXiv:math/0303191 · doi:10.1088/0264-9381/20/20/305
Abstract
A hyperkähler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyperkähler 4-metric metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant Schrödinger and the Hamilton-Jacobi equation is separable and the system integrable.
10 pages Latex