On the structure tensors of almost contact B-metric manifolds

TL;DR

This paper investigates the structure tensors of almost contact B-metric manifolds, decomposing their covariant derivatives into invariant components and analyzing specific cases and examples.

Contribution

It provides a detailed decomposition of the structure tensor space and characterizes its components, especially in the 3-dimensional case.

Findings

Decomposition of the structure tensor space into orthogonal invariant subspaces.

Explicit determination of tensor components for almost contact B-metric manifolds.

Analysis of the 3-dimensional case with illustrative examples.

Abstract

The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspaces with respect to the action of the structure group is used. We determine the corresponding components of the structure tensor and consider the case of the lowest dimension 3 of the studied manifolds. Some examples are commented.