Abstract
We introduce the concept of a Clifford–Weyl structure on a conformal manifold, which consists of an even Clifford structure parallel with respect to the tensor product of a metric connection on the Clifford bundle and a Weyl structure on the manifold. We show that the Weyl structure is necessarily closed except for some “generic” low-dimensional instances, where explicit examples of non-closed Clifford–Weyl structures can be constructed.
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Hadfield, C., Moroianu, A. Local geometry of even clifford structures on conformal manifolds. Ann Glob Anal Geom 54, 301–313 (2018). https://doi.org/10.1007/s10455-018-9602-8
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DOI: https://doi.org/10.1007/s10455-018-9602-8