Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure

TL;DR

This paper introduces and analyzes a pair of specialized affine connections on almost contact B-metric manifolds, characterizing their classes and curvature properties to deepen understanding of their geometric structure.

Contribution

It presents a novel pair of associated Schouten-van Kampen connections adapted to almost contact B-metric structures, linking connection properties with manifold classifications.

Findings

Characterization of basic classes of almost contact B-metric manifolds.

Curvature properties of the introduced connections.

Insights into the geometric structure via non-symmetric connections.

Abstract

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of almost contact B-metric manifolds are characterized. Curvature properties of the considered connections are obtained.