Hyperspheres in Euclidean and Minkowski 4-spaces as almost paracontact almost paracomplex Riemannian manifolds

TL;DR

This paper investigates hyperspheres in 4-dimensional Euclidean and Minkowski spaces, constructing and analyzing almost paracontact almost paracomplex Riemannian structures, and classifying their geometric properties.

Contribution

It introduces new structures on hyperspheres in Euclidean and Minkowski spaces and characterizes their geometric properties within a specific classification framework.

Findings

Structures are successfully constructed on hyperspheres in both spaces.

The manifolds are classified and their geometric properties are characterized.

The study enhances understanding of paracontact and paracomplex structures in low dimensions.

Abstract

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension are studied. Such structures are constructed on hyperspheres in 4-dimensional spaces, Euclidean and pseudo-Euclidean, respectively. The obtained manifolds are studied and characterised in terms of the classification used and their geometric properties.