Local Classification and Examples of an Important Class of Paracontact Metric Manifolds


Verónica Martín-Molina




We study paracontact metric ($\kappa,\mu$)-spaces with $\kappa=-1$, equivalent to $h^2=0$ 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 ($-1,\mu$)-spaces with tensor $h$ of non-constant rank, which were not known to exist until now.