Paracontact metric manifolds without a contact metric counterpart

We study non-paraSasakian paracontact metric $(κ,μ)$-spaces with $κ=-1$ (equivalent to $h^2=0$ but $h\neq0$). 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 $h$.

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