Invariant cocalibrated $G_2$-structures on nilmanifolds

TL;DR

This paper classifies nilmanifolds that admit invariant cocalibrated $G_2$-structures, providing a comprehensive understanding of their geometric properties and potential applications in differential geometry.

Contribution

It offers a complete classification of nilmanifolds with invariant cocalibrated $G_2$-structures, a previously unresolved problem in the field.

Findings

Identified all nilmanifolds supporting invariant cocalibrated $G_2$-structures

Provided explicit descriptions of these structures on classified nilmanifolds

Enhanced understanding of $G_2$-geometry in the context of nilmanifolds

Abstract

We classify nilmanifolds admitting invariant cocalibrated $G_2$-structures