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

TL;DR

This paper investigates critical normal sections of 2D immersions in higher-dimensional Euclidean spaces, establishing bounds on torsion coefficients and extending previous work on surfaces in R^4.

Contribution

It introduces bounds for torsion coefficients of normal sections in non-flat normal bundles and advances the theory of 2D immersions in higher dimensions.

Findings

Established upper bounds for torsion coefficients.

Extended previous results on surfaces in R^4.

Analyzed critical normal sections for total torsion functional.

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 $\mathbb R^4.$