Second order contact of minimal surfaces

Abstract

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 dierential form on Q n 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, andM is equal to the real part of the integral of over C. The complete minimal surfaces of nite topological type and with at points at innity correspond to the algebraic curves in Q.