Parallel spinors and holonomy groups

Andrei Moroianu (1) , Uwe Semmelmann (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Fachbereich Mathematik [Hamburg]

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.

Mots clés: Infinitesimal isometry; Killing spinor; Sasakian structure

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Uwe Semmelmann. Parallel spinors and holonomy groups. Journal of Mathematical Physics, 2000, 41, pp.2395-2402. ⟨hal-00126070⟩