Weierstrass representation for surfaces in multidimensional spaces

Michel Grundland

Centre de Recherches Mathematiques
Universite de Montreal
C.P.6128, succ. Centre-Ville
Montreal, Quebec
H3C 3J7, Canada

Abstract

We introduce a Weierstrass-type system of equations corresponding to CP^N harmonic maps, which generalize the systems previously constructed for CP^1 and CP^2. We use a set of conserved quantities for CP^N model in order to suggest a certain geometric interpretation of the generalized Weierstrass system describing surfaces immersed in multidimensional spaces.