On the existence of homogeneous solitons of gradient type for the G_{2}-Laplacian flow

Abstract

In this note, we prove the existence of homogeneous gradient solitons for the G 2 _2 -Laplacian flow by providing the first known example of this type. This result singles out the G 2 _2 -Laplacian flow as the first known geometric flow admitting homogeneous gradient solitons on spaces that are one-dimensional extensions in the sense of Petersen and Wylie [Differential Geom. Appl. 84 (2022), Paper No. 101929, 29].