Canonical fibrations of contact metric (κ,μ)-spaces

Abstract

We present a classification of the complete, simply connected, contact metric (κ, µ)-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 (κ, µ)-spaces with Boeckx invariant less than −1. (2000): Primary 53C25, 53D10; Secondary 53C35, 53C30. Mathematics Subject Classification

Some Non-Compactness Results for Locally Homogeneous Contact Metric Manifolds

“…The simply connected, complete, non Sasakian (κ, μ)-spaces are all homogeneous and are completely classified (see [5,9,11]) and, considering two such spaces equivalent up to D a -homothetic deformations, they form a oneparameter family parametrized by R. This family contains the tangent sphere bundles T 1 S where S is a Riemannian space form. The classification relies on a result of Boeckx [5], stating that the number…”