A classification of the torsion tensors on almost contact manifolds with B-metric

TL;DR

This paper classifies the torsion tensors on almost contact manifolds with B-metric into 15 invariant subspaces and characterizes three known structure-preserving connections within this framework.

Contribution

It introduces a new decomposition of torsion tensors into 15 orthogonal invariant subspaces and characterizes known connections accordingly.

Findings

Torsion tensors are decomposed into 15 invariant subspaces.

Three known structure-preserving connections are characterized.

The classification aids in understanding the geometry of almost contact B-metric manifolds.

Abstract

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.