The Moutard transformation of two-dimensional Dirac operators and the Mobius geometry

Abstract

We describe the action of the (Mobius) inversion on the data of the Weierstrass representation of surfaces in the three-space and show that the Moutard transformation of two-dimensional Dirac operators has a geometrical meaning: it maps the potential $U$ of a surface $S$ into the potential of its inversion.

17 pages

References in corpus (1)

• Conformal invariant functionals of immersions of tori into R^3