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

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

2009-01-23

arxiv.org/abs/0901.3647v2

Mathematics

Differential Geometry

24 pages

Scientific paper

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.

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