Generalized G_2-manifolds and SU(3)-structures

TL;DR

This paper constructs a compact 7-dimensional manifold with a weakly integrable generalized G_2-structure and explores conditions under which certain SU(3)-structures induce strongly integrable generalized G_2-structures on product manifolds.

Contribution

It provides the first known example of a compact 7-manifold with a weakly integrable generalized G_2-structure and analyzes the link between SU(3)-structures and integrability of generalized G_2-structures.

Findings

Constructed a compact 7-dimensional manifold with a weakly integrable generalized G_2-structure.

Identified conditions on SU(3)-structures that lead to strongly integrable generalized G_2-structures on product manifolds.

Analyzed the role of a non-trivial 3-form in the integrability of these structures.

Abstract

We construct a compact example of 7- dimensional manifold endowed with a weakly integrable generalized G_2-structure with respect to a closed and non trivial 3-form. Moreover, we investigate which type of SU(3)-structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G_2-structure with respect to a non trivial 3-form on the product $N \times S^1$.