On critical normal sections for two-dimensional immersions in $${\mathbb R^{n+2}}$$

Abstract

We study orthonormal normal sections of two-dimensional immersions in \({\mathbb R^{n+2}, n\ge 2}\) , which are critical for a functional of total torsion and which we call Coulomb sections. In particular, we establish upper bounds for the torsion coefficients in the case of non-flat normal bundles. With these notes we continue a foregoing paper on surfaces in \({\mathbb R^4.}\)