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

Eugenia Loiudice and Antonio Lotta

Vol. 300 (2019), No. 1, 39–63

DOI: 10.2140/pjm.2019.300.39

Abstract

We present a classification of the complete, simply connected, contact metric $\left(\kappa ,\mu \right)$-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 paracomplexification of a sphere or of a hyperbolic space. In particular, we obtain a new homogeneous representation of the contact metric $\left(\kappa ,\mu \right)$-spaces with Boeckx invariant less than $-1$.

Keywords

contact metric $(\kappa,\mu)$-space, regular contact manifold

Mathematical Subject Classification 2010

Primary: 53C25, 53D10

Secondary: 53C30, 53C35

Milestones

Received: 9 April 2017

Revised: 31 January 2018

Accepted: 17 July 2018

Published: 20 July 2019