Almost contact metric 5-manifolds and connections with torsion

TL;DR

This paper classifies 5-dimensional almost contact metric manifolds based on their intrinsic torsion, explores conditions for compatible metric connections with various torsion types, and examines explicit examples.

Contribution

It provides a classification scheme for these manifolds and characterizes the existence of specific metric connections with torsion.

Findings

Classification of almost contact metric structures by intrinsic torsion

Necessary and sufficient conditions for metric connections with torsion

Explicit examples illustrating the theoretical results

Abstract

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and sufficient conditions for the existence of metric connections with vectorial, totally skew-symmetric or traceless cyclic torsion that are compatible with the almost contact metric structure. Finally, we examine explicit examples of almost contact metric 5-manifolds from this perspective.