Asian Journal of Mathematics

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

Florin Belgun and Andrei Moroianu

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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.

Article information

Source
Asian J. Math., Volume 15, Number 4 (2011), 499-520.

Dates
First available in Project Euclid: 12 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1331583345

Mathematical Reviews number (MathSciNet)
MR2853646

Zentralblatt MATH identifier
1271.53038

Subjects
Primary: 53A30: Conformal differential geometry 53C05: Connections, general theory 53C29: Issues of holonomy

Keywords
Conformal products conformally parallel forms Weyl structures reducible holonomy

Citation

Belgun, Florin; Moroianu, Andrei. Weyl-Parallel Forms, Conformal Products and Einstein-Weyl Manifolds. Asian J. Math. 15 (2011), no. 4, 499--520. https://projecteuclid.org/euclid.ajm/1331583345


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