On branch points of superminimal surfaces in 4-manifolds (Q5950241)

The superminimal surfaces in an oriented Riemannian 4-manifold are considered as the best possible Riemannian analogues of complex curves in Kähler surfaces [see \textit{P. Gauduchon}, Bull. Soc. Math. Fr. 114, 447-508 (1986; Zbl 0623.53025)]. It is proved that, in a neighborhood of a branch point, a right (resp. left) superminimal map of the complex disc into a 4-manifold can be made holomorphic (resp. antiholomorphic) by composing with orientation preserving diffeomorphisms of the domain and the image.