Parallel spinors and holonomy groups
Differential Geometry
2019-01-08 v1 Algebraic Geometry
Abstract
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.
Cite
@article{arxiv.math/9903062,
title = {Parallel spinors and holonomy groups},
author = {Andrei Moroianu and Uwe Semmelmann},
journal= {arXiv preprint arXiv:math/9903062},
year = {2019}
}
Comments
10 pages, LaTeX2e