Almost Contact Metric Structures Induced by $G_2$ Structures

TL;DR

This paper investigates how $G_2$ structures induce almost contact metric structures on manifolds, classifies possible structures, and provides concrete examples to illustrate these geometric configurations.

Contribution

It introduces a new approach to induce almost contact metric structures from $G_2$ structures and classifies their possible types, expanding understanding of these geometric relations.

Findings

Identification of classes of almost contact metric structures induced by $G_2$ structures

Examples demonstrating the induced structures

Results on the geometric properties of these structures

Abstract

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.