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Annals of Global Analysis and Geometry

, Volume 54, Issue 2, pp 301–313 | Cite as

Local geometry of even clifford structures on conformal manifolds

  • Charles Hadfield
  • Andrei Moroianu
Article
  • 58 Downloads

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.

Keywords

Even Clifford structures Conformal manifolds Weyl structures 

Mathematics Subject Classification

Primary 53C26 53A30 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.École Normale SupérieureParis Cedex 05France
  2. 2.Laboratoire de Mathématiques de Versailles, UVSQ, CNRSUniversité, Paris-SaclayVersaillesFrance

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