Gauss maps of harmonic and minimal great circle fibrations
Differential Geometry
2022-04-27 v2
Abstract
We investigate Gauss maps associated to great circle fibrations of . We show that the associated Gauss map to such a fibration is harmonic (respectively minimal) if and only if the unit vector field generating the great circle foliation is harmonic (respectively minimal). These results can be viewed as analogues of the classical theorem of Ruh and Vilms about the harmonicity of the Gauss map of a minimal submanifold in the euclidean space. Moreover, we prove that a harmonic or minimal unit vector field in with great circle integral curves is a Hopf vector field.
Keywords
Cite
@article{arxiv.2203.12404,
title = {Gauss maps of harmonic and minimal great circle fibrations},
author = {Ioannis Fourtzis and Michael Markellos and Andreas Savas-Halilaj},
journal= {arXiv preprint arXiv:2203.12404},
year = {2022}
}
Comments
The revised version contains new results concerning minimal unit vector fields. The presentation of the paper is improved and typos are fixed