Second order Contact of Minimal Surfaces

Details Second order Contact of Minimal Surfaces Second order Contact of Minimal Surfaces

2002-01-18

arxiv.org/abs/math/0201171v1

Mathematics

Differential Geometry

LaTeX2e; Submitted to Journal of Differential Geometry, June 15, 2001

Scientific paper

The minimal surface equation $Q$ in the second order contact bundle of $R^3$, modulo translations, is provided with a complex structure and a canonical vector-valued holomorphic differential form $Omega$ on $Q\0$. The minimal surfaces $M$ in $R^3$ correspond to the complex analytic curves $C$ in $Q$, where the derivative of the Gauss map sends $M$ to $C$, and $M$ is equal to the real part of the integral of $\Omega$ over $C$. The complete minimal surfaces of finite topological type and with flat points at infinity correspond to the algebraic curves in $Q$.

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