Stable Plane-Gauss Maps on Closed Orientable Surfaces

Abstract

The aim of this paper is to study the couple of stable plane Gauss maps f = (f2, f3): M→ R^2×S^2 from a global point of view, where M is a smooth closed orientable surface, f2 is a projection and f3 is Gauss map. We associate this maps a pair of MF-graph. We will study their properties, giving conditions on the graphs that can be realized by pairs of maps with couples from pre-determined singular sets.

Keywords

• Closed surfaces
• graphs
• stable maps