Local classification and examples of an important class of paracontact metric manifolds

Abstract

We study paracontact metric ( , μ)-spaces with = −1, equivalent to h2 = 0 but not h = 0. In particular, we will give an alternative proof of Theorem 3.2 of [11] and present examples of paracontact metric (−1, 2)-spaces and (−1, 0)-spaces of arbitrary dimension with tensor h of every possible constant rank. We will also show explicit examples of paracontact metric (−1, μ)- spaces with tensor h of non-constant rank, which were not known to exist until now