On the classification of almost contact metric manifolds

TL;DR

This paper proves the non-existence of certain almost contact metric structures on higher-dimensional manifolds and explores the relationships among their intrinsic torsion components to describe relevant form derivatives.

Contribution

It establishes the non-existence of specific contact metric structures and analyzes the intrinsic torsion interrelations in almost contact metric geometry.

Findings

Certain contact metric structures do not exist in higher dimensions.

Interrelations among intrinsic torsion components are characterized.

Exterior derivatives of key forms are described in this context.

Abstract

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and Gonz\'alez-D\'avila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to describe the exterior derivatives of some relevant forms in the context of almost contact metric geometry.