Weyl-parallel forms, conformal products and Einstein-Weyl manifolds

TL;DR

This paper explores Weyl structures on conformal manifolds, introduces conformal products, classifies Weyl manifolds with parallel forms, and describes a new class of Einstein-Weyl 4-manifolds.

Contribution

It defines conformal products of conformal structures and classifies Weyl manifolds with parallel forms, advancing understanding of Einstein-Weyl geometries.

Findings

Classification of Weyl manifolds with parallel forms

Description of holonomy of Weyl connections on conformal products

Introduction of a new class of Einstein-Weyl 4-manifolds

Abstract

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the adapted Weyl connection on conformal products. As an application we describe a new class of Einstein-Weyl manifolds of dimension 4.