Gravitational instantons, confocal quadrics and separability of the Schr dinger and Hamilton–Jacobi equations

2003/03/16 by G. W. Gibbons · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Geometry and complex manifolds #hep-th #math.DG #msc:53C26

paper · pdf · doi:10.1088/0264-9381/20/20/305

published as Class.Quant.Grav.20:4401-4408,2003 · 10 pages Latex

arxiv created 2003/03/16 · openalex publication_date 2003/09/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A hyperk"ahler 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 hyperk"ahler 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 Schr"odinger and the Hamilton-Jacobi equation is separable and the system integrable.

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