Area minimizing unit vector fields on antipodally punctured unit 2-sphere and minimally immersed Klein Bottles
Differential Geometry
2020-11-11 v1
Abstract
We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere depending on the length of an ellipse determined by the indexes of its singularities. In addition, for minimizing vector fields having specific pair of indexes, we show that their image coincides with the image of minimally immersed Klein bottles.
Keywords
Cite
@article{arxiv.2011.05183,
title = {Area minimizing unit vector fields on antipodally punctured unit 2-sphere and minimally immersed Klein Bottles},
author = {Fabiano Brito and Jackeline Conrado and Adriana Nicoli and Ícaro Gonçalves},
journal= {arXiv preprint arXiv:2011.05183},
year = {2020}
}