Almost paracontact almost paracomplex Riemannian manifolds as extensions of 2-dimensional space-forms

Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional Riemannian space-form. Their metric is obtained in two ways: as a cone metric and as a hyperbolic extension of the metric of the underlying paracomplex 2-manifold. The resulting manifolds are studied and characterized in terms of the classification used and their curvature properties.