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

Marina Ville (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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 link at infinity; we derive the 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.

Mots clés: Courbure; Nœuds; Surfaces minimales complètes

Domaines: Géométrie différentielle [math.DG]

Marina Ville. A link at infinity for minimal surfaces in $\mathbb{R}^4$. 2014. ⟨hal-01059935⟩