Abstract. We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentzian) Ricci solitons are necessarily trivial, that is, K-contact and Einstein, the paracontact metric case allows nontrivial examples. Both homogeneous and inhomogeneous nontrivial three-dimensional examples are explicitly described. Finally, we correct the main result of [1], concerning three-dimensional normal paracontact Ricci solitons.

For an arbitrary three-dimensional normal paracontact metric structure equipped with a Killing characteristic vector field, we obtain a complete classification of the magnetic curves of the corresponding magnetic field. In particular, this yields to a complete description of magnetic curves for the characteristic vector field of threedimensional paraSasakian and paracosymplectic manifolds. Explicit examples are described for the hyperbolic Heisenberg group and a paracosymplectic model.

We study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

We completely characterize cosymplectic and α-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in dimension five for cosymplectic, K-cosymplectic and coKähler Lie algebras.

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