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

Abstract

We study orthonormal normal sections of two-dimensional immersions in ${\mathbb{R}}^{n+2},$ $n\ge 2$, at which these sections are critical for a functional of total torsion. 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 ${\mathbb{R}}^4.$