Local Geometry of Even Clifford Structures on Conformal Manifolds

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.

15 pages

References in corpus (5)

• Centralizers of spin subalgebras
• Almost even-Clifford hermitian manifolds with large automorphism group
• Clifford systems in octonionic geometry
• A note on the geometry and topology of almost even-Clifford Hermitian manifolds
• Rigidity and Vanishing Theorems for Almost Even-Clifford Hermitian Manifolds

Cited by in corpus (1)

• Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles