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Updated: Feb 12, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Magnetic zero-modes, vortices and Cartan geometry
Calum Ross1,2, Bernd J Schroers1,2
11Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS UK.
Abstract:
We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.
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