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On generalized Gauduchon metrics

Part of: Global differential geometry Compact analytic spaces

Published online by Cambridge University Press:  21 March 2013

Anna Fino  and
Luis Ugarte
Anna Fino
Affiliation:
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy (annamaria.fino@unito.it)
Luis Ugarte
Affiliation:
Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain (ugarte@unizar.es)
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Abstract

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We study a class of Hermitian metrics on complex manifolds, recently introduced by Fu, Wang and Wu, which are a generalization of Gauduchon metrics. This class includes the class of Hermitian metrics for which the associated fundamental 2-form is ∂∂-closed. Examples are given on nilmanifolds, on products of Sasakian manifolds, on S1-bundles and via the twist construction introduced by Swann.

Keywords

Hermitian structureGauduchon metricKähler manifolds

MSC classification

Secondary: 53C55: Hermitian and Kählerian manifolds 32J27: Compact Kähler manifolds 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 733 - 753
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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