Weyl-Parallel Forms, Conformal Products and Einstein-Weyl Manifolds

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.

Keywords

Conformal products, conformally parallel forms, Weyl structures, reducible holonomy

2010 Mathematics Subject Classification

53A30, 53C05, 53C29

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Published 17 April 2012