Paracontact metric manifolds without a contact metric counterpart

Abstract

We study non-paraSasakian paracontact metric $(\kappa ,\mu )$-spaces with $\kappa =-1$ (equivalent to $h^2=0$ but $h\ne 0$). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of $h$. We will also give explicit examples of every possible constant rank of $h$.

12 pages; several corrections have been made in this version