Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric

TL;DR

This paper constructs a natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric, explores the class of such manifolds, and investigates curvature properties under specific conditions.

Contribution

It introduces a new natural connection with skew-symmetric torsion on a specific class of manifolds and analyzes its curvature characteristics.

Findings

Identification of the class of manifolds admitting this connection

Curvature properties when the curvature tensor mimics Levi-Civita tensor

Conditions for torsion tensor to be parallel

Abstract

A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this connection, when the corresponding curvature tensor has the properties of the curvature tensor for the Levi-Civita connection and the torsion tensor is parallel, are obtained.