Harmonic Gauss maps of submanifolds of arbitrary codimension of the Euclidean space and sphere and some applications

TL;DR

This paper investigates conditions under which Gauss maps of submanifolds in Euclidean space and spheres are harmonic, providing results on their existence and applications to special classes like CMC hypersurfaces and isoparametric submanifolds.

Contribution

It establishes new results on the existence and non-existence of harmonic Gauss maps for submanifolds of arbitrary codimension, with applications to geometric problems.

Findings

Conditions for harmonic Gauss maps in Euclidean space and spheres

Results on CMC hypersurfaces and isoparametric submanifolds

Applications to geometric analysis of submanifolds

Abstract

It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and isoparametric submanifolds are obtained too.