Canonical fibrations of contact metric \((\kappa,\mu)\)-spaces

We present a classification of the complete, simply connected, contact metric \((\kappa,\mu)\)-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx invariant, it turns out that the base is a complexification or...

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Bibliographic Details
Published inarXiv.org
Main Authors Loiudice, Eugenia, Lotta, Antonio
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.04.2017
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Mathematics - Differential Geometry
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Summary:We present a classification of the complete, simply connected, contact metric \((\kappa,\mu)\)-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx invariant, it turns out that the base is a complexification or a para-complexification of a sphere or of a hyperbolic space. In particular, we obtain a new homogeneous representation of the contact metric \((\kappa,\mu)\)-spaces with Boeckx invariant less than \(-1\).
ISSN:2331-8422
DOI:10.48550/arxiv.1704.01310