On Algebraic Minimal Surfaces in R3 Deriving from Charge 2 Monopole Spectral Curves
Small, Anthony (2005) On Algebraic Minimal Surfaces in R3 Deriving from Charge 2 Monopole Spectral Curves. International Journal of Mathematics, 16 .
We give formulae for minimal surfaces in R3 deriving, via classical osculation duality, from elliptic curves in a line bundle over P1. Specialising to the case of charge 2 monopole spectral curves we find that the distribution of Gaussian curvature on the auxiliary minimal surface reflects the monopoleâs structure. This is elucidated by the behaviour of the surfaceâs Gauss map.
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