Almost contact B-metric manifolds as extensions of a 2-dimensional space-form

TL;DR

This paper studies almost contact B-metric manifolds formed as products of a real line and a 2D complex space, analyzing their classification and curvature properties using two different metric generation methods.

Contribution

It introduces two methods for constructing B-metrics on such manifolds and characterizes their properties within the Ganchev-Mihova-Gribachev classification.

Findings

Manifolds are classified within the Ganchev-Mihova-Gribachev scheme.

Curvature properties of the constructed manifolds are characterized.

Different metric generation methods lead to distinct manifold properties.

Abstract

The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are characterised with respect to the Ganchev-Mihova-Gribachev classification and their basic curvature properties.