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An extension to higher dimensions of the Bel-Debever characterization of theWeyl tensor is considered. This provides algebraic conditions that uniquelydetermine the multiplicity of a Weyl aligned null direction (WAND), and thusthe principal Weyl type, in a frame independent way. The specification ofseveral "subtypes" is also encompassed by the criteria. We further comment on aCartan-like geometrical interpretation of WANDs in terms of their invarianceproperties under parallel transport around infinitesimal loops. As a result,restrictions on the algebraic types permitted in spacetimes that admit arecurrent/covariantly constant vector field are outlined.

Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions