The spinorial energy functional: solutions of the gradient flow on Berger spheres
Differential Geometry
2017-05-24 v2
Abstract
We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Wei{\ss}, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, for special cases, we prove that the volume-normalized standard 3-sphere together with a Killing spinor is a stable critical point of the volume-normalized version of the flow. Our results also include an example of a critical point of the volume-normalized flow on the 3-sphere, which is not a Killing spinor.
Keywords
Cite
@article{arxiv.1510.04865,
title = {The spinorial energy functional: solutions of the gradient flow on Berger spheres},
author = {Johannes Wittmann},
journal= {arXiv preprint arXiv:1510.04865},
year = {2017}
}
Comments
Minor typo corrected, added a sentence in the abstract