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

Abstract

We study paracontact metric (k,?)-spaces with k = -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,?)-spaces with tensor h of non-constant rank, which were not known to exist until now.