Parallel spinors and holonomy groups (Q2737940)

The authors complete the classification of holonomy groups admitting parallel spinors given by \textit{M. Y. Wang} [Ann. Global Anal. Geom. 13, 31-42 (1995; Zbl 0826.53041)], by showing that on a given \(n\)-dimensional Riemannian manifold spin structures with parallel spinors are in a one-to-one correspondence with lifts to \(\text{Spin}_n\) of the Riemannian holonomy group having fixed points on the spin representation space. In particular, they also exhibit the first example of compact manifolds having two different spin structures with parallel spinors.NEWLINENEWLINENEWLINEContents include: an introduction; preliminaries; Wang's holonomy criterion; spin structures induced by holonomy bundles; examples and further remarks.