Canonical-type connection on almost contact manifolds with B-metric

TL;DR

This paper constructs a canonical-type connection on almost contact manifolds with B-metric, analyzes its torsion invariance under conformal transformations, and characterizes manifold classes via this torsion.

Contribution

It introduces a canonical-type connection on almost contact B-metric manifolds and studies its torsion properties and invariance under transformations.

Findings

Torsion of the connection is invariant under a subgroup of conformal transformations.

Basic classes of manifolds are characterized by the torsion of this connection.

The connection provides a new tool for classifying almost contact B-metric manifolds.

Abstract

The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.