CR Weyl geometry and connections of the canonical bundle

Abstract

A nondegenerate CR manifold has a natural conformal class consisting of hermitian forms, which are called Levi forms, on the hyperdistribution. It is important to study the objects on CR manifolds which are independent of the choice of Levi forms. A CR Einstein-Weyl structure defined in [8] is one of such objects. Our purpose is to find nondegenerate CR manifolds with CR Einstein-Weyl structures.

In this paper, we shall obtain many examples of CR Einstein-Weyl manifolds. These examples are actually derived from the fact that CR Einstein-Weyl structures are closely concerned with connections of the canonical bundle of CR manifolds.