#### Vol. 300, No. 1, 2019

 Recent Issues Vol. 304: 1 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
Canonical fibrations of contact metric $(\kappa,\mu)$-spaces

### Eugenia Loiudice and Antonio Lotta

Vol. 300 (2019), No. 1, 39–63
##### 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