# Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

## TL;DR

This paper explores 3-dimensional Lie groups equipped with almost paracontact almost paracomplex Riemannian structures, analyzing their curvature properties and providing explicit examples to illustrate the theoretical findings.

## Contribution

It constructs and studies 3D Lie group manifolds with these structures, offering new insights into their geometric properties and curvature characteristics.

## Key findings

- Curvature properties of the constructed manifolds are characterized.
- Explicit examples support the theoretical analysis.
- New class of Lie group manifolds with these structures is introduced.

## Abstract

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds are investigated. An example is commented as support of obtained results.