# Structures de Weyl admettant des spineurs parallèles

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00126043
Contributor : Andrei Moroianu <>
Submitted on : Tuesday, January 23, 2007 - 2:36:11 PM
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• HAL Id : hal-00126043, version 1

### Citation

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

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