Parallel spinors and holonomy groups

Details Parallel spinors and holonomy groups Parallel spinors and holonomy groups

1999-03-11

arxiv.org/abs/math/9903062v1

Journal of Mathematical Physics 41 (2000), 2395-2402

Mathematics

Differential Geometry

10 pages, LaTeX2e

Scientific paper

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.

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