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

TL;DR

This paper investigates 3-dimensional almost paracontact Riemannian manifolds with paracomplex structures, constructed as extensions of 2D space-forms, analyzing their metrics and curvature properties.

Contribution

It introduces a method to construct such manifolds as products of a real line and 2D space-forms, exploring their geometric and curvature characteristics.

Findings

Manifolds constructed as cone and hyperbolic extensions

Characterization in terms of classification schemes

Curvature properties of the extended manifolds

Abstract

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.