Stable Plane-Gauss Maps on Closed Orientable Surfaces

ABSTRACT

The aim of this paper is to study the couple of stable plane Gauss maps $f=(f_2,f_3):M\to {\mathrm{ℝ}}^2\times {\mathbb{S}}^2$ from a global point of view, where M is a smooth closed orientable surface, f ₂ is a projection and f ₃ 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