A link at infinity for minimal surfaces in ${\mathbb{R}}^4$

Abstract

We look at complete minimal surfaces of finite total curvature in ${\mathbb{R}}^4$. Similarly to the case of complex curves in ${\mathbb{C}}^2$ we introduce their {\it link at infinity}; we derive the {\it writhe number at infinity} which gives a formula for the total normal curvature of the surface. The knowledge of the link at infinity can sometimes help us determine if a surface has self-intersection and we illustrate this idea by looking at genus zero surfaces of small total curvature.

References in corpus (1)

• Milnor numbers for 2-surfaces in 4-manifolds