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.

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Abstract

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 monopole’s structure. This is elucidated by the behaviour of the surface’s Gauss map.

Item Type: Article
Keywords: Algebraic minimal surfaces; R3; Charge 2 Monopole Spectral Curves; Gauss map;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 718
Depositing User: Dr. Anthony Small
Date Deposited: 05 Oct 2007
Journal or Publication Title: International Journal of Mathematics
Publisher: World Scientific Publishing
Refereed: Yes
URI:

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