Space-like and time-like hyperspheres in real pseudo-Riemannian 4-spaces with almost contact B-metric structures

TL;DR

This paper investigates space-like and time-like hyperspheres in 4-dimensional pseudo-Riemannian spaces with specific signatures, equipped with almost contact B-metric structures, and characterizes their geometric properties.

Contribution

It introduces a geometric characterization of hyperspheres with almost contact B-metric structures in pseudo-Riemannian 4-spaces with signatures (3,1) and (2,2).

Findings

Geometric properties of hyperspheres are explicitly described.

Manifolds with almost contact B-metric structures are characterized.

Different signatures lead to distinct geometric structures.

Abstract

There are considered 4-dimensional pseudo-Riemannian spaces with inner products of signature (3,1) and (2,2). The objects of investigation are space-like and time-like hyperspheres in the respective cases. These hypersurfaces are equipped with almost contact B-metric structures. The constructed manifolds are characterized geometrically.