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

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.