Special types of locally conformal closed G$_2$-structures

TL;DR

This paper explores various classes of G$_2$-structures defined by locally conformal closed 3-forms, providing classifications on Lie groups and examples on compact manifolds, inspired by symplectic geometry analogies.

Contribution

It offers a complete characterization of invariant exact locally conformal closed G$_2$-structures on simply connected Lie groups and presents new examples on compact manifolds.

Findings

Complete classification of invariant exact locally conformal closed G$_2$-structures on Lie groups

Construction of examples of compact manifolds with different locally conformal closed G$_2$-structures

Analogy with locally conformal symplectic geometry

Abstract

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact locally conformal closed G$_2$-structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G$_2$-structures.