Remarks on homogeneous solitons of the $\protect \mathrm{G}_{2}$-Laplacian flow

Abstract

We show the existence of expanding solitons of the $\mathrm{G}_2$-Laplacian flow on non-solvable Lie groups, and we give the first example of a steady soliton that is not an extremally Ricci pinched $\mathrm{G}_2$-structure.