# Conformal geodesics on gravitational instantons

@article{Dunajski2019ConformalGO, title={Conformal geodesics on gravitational instantons}, author={Maciej Dunajski and Paul Tod}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2019}, volume={173}, pages={123 - 154} }

Abstract We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the SO(3)–invariant gravitational instantons. On a hyper–Kähler four–manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self–dual magnetic field. In the case of the anti–self–dual Taub NUT instanton we integrate these equations completely by separating the Hamilton–Jacobi equations, and finding a commuting set of first…

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