Structures de Weyl admettant des spineurs parallèles

Andrei Moroianu (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We prove that given a Weyl structure $D$ on a spin manifold $(M^n,g)$, the existence of a non-zero $D$-parallel spinor on $M$ implies that $D$ is closed for $n\ne4$. The same statement is true for $n=4$ if $M$ is compact. We give non-compact examples of 4-manifolds admitting parallel spinors with respect to non-closed Weyl structures.

Mots clés: spineurs parallèles; structures de Weyl; structures hermitiennes

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu. Structures de Weyl admettant des spineurs parallèles. Bulletin de la société mathématique de France, 1996, 124, pp.685-695. ⟨hal-00126043⟩