Natural connections with torsion expressed by the metric tensors on almost contact manifolds with B-metric

TL;DR

This paper explores a family of linear connections on almost contact manifolds with B-metric, identifying canonical and zero-parameter connections that preserve the manifold's structures.

Contribution

It introduces a four-parameter family of structure-preserving connections on almost contact B-metric manifolds, including canonical and zero-parameter special cases.

Findings

Identified a four-parameter family of connections preserving structures

Determined the canonical-type connection within this family

Described the zero-parameter connection as a special case

Abstract

On a main class of the almost contact manifolds with B-metric, it is described the family of the linear connections preserving the manifold's structures by 4 parameters. In this family there are determined the canonical-type connection and the connection with zero parameters.