Local geometry of even Clifford structures on conformal manifolds (Q1994070)

The authors study even Clifford structures over conformal manifolds. They introduce the notion of a Clifford-Weyl structure. This notion consists of the following data: a conformal manifold \((M,c)\) with a Weyl structure \(D\) and a Clifford structure \((E, h, \phi)\) parallel with respect to the Weyl structure \(D\) and a metric connection on \(E\). In the case when \(D\) is exact, i.e., when it is the Levi-Civita connection of some metric in \(c\), this notion becomes equivalent to that of a parallel even Clifford structure on a Riemannian manifold. The authors explore the conditions under which \(D\) is closed. They show that in the six ``generic'' low-dimensional cases the existence of a Clifford-Weyl structure does not force the Weyl connection \(D\) to be closed, and in all other ``non-generic'' cases \(D\) is closed. The authors give explicit examples of Clifford-Weyl structures with non-closed associated Weyl structures in each ``generic'' case.