Local Geometry of Even Clifford Structures on Conformal Manifolds

TL;DR

This paper introduces Clifford-Weyl structures on conformal manifolds, showing that they are generally closed Weyl structures except in specific low-dimensional cases where non-closed examples exist.

Contribution

It defines Clifford-Weyl structures on conformal manifolds and characterizes when the associated Weyl structure is closed or non-closed, including explicit low-dimensional examples.

Findings

Weyl structure is necessarily closed in most cases.

Explicit non-closed examples are constructed in low dimensions.

Clifford-Weyl structures are a new geometric concept 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.