Harmonic spinors and local deformations of the metric
Differential Geometry
2016-03-03 v3
Abstract
Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.
Keywords
Cite
@article{arxiv.0903.4544,
title = {Harmonic spinors and local deformations of the metric},
author = {Bernd Ammann and Mattias Dahl and Emmanuel Humbert},
journal= {arXiv preprint arXiv:0903.4544},
year = {2016}
}
Comments
minor changes, to appear in Mathematical Research Letters