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TitleOn the characterization of non-degenerate foliations of pseudo-Riemannian manifolds with conformally flat leaves
Author(s)García-Parrado Gómez-Lobo, Alfonso
KeywordsFoliation theory
Conformal geometry
Issue date4-Jun-2013
PublisherAIP Publishing
JournalJournal of mathematical physics
Abstract(s)A necessary and sufficient condition for the leaves of a non-degenerate foliation of a pseudo-Riemannian manifold to be conformally flat is developed. The condition mimics the classical condition of the vanishing of the Weyl or Cotton tensor establish- ing the conformal flatness of a pseudo-Riemannian manifold in the sense that it is also formulated in terms of the vanishing of certain tensors. These tensors play the role of the Weyl or the Cotton tensors and they are defined in terms of the curvature of a linear torsion-free connection (the bi-conformal connection).
DescriptionPublished online 4 June 2013
Publisher version
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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