On the existence of homogeneous solitons of gradient type for the G$_2$-Laplacian flow

TL;DR

This paper establishes the existence of the first known homogeneous gradient solitons for the G$_2$-Laplacian flow, highlighting a new class of solutions in geometric flow theory on one-dimensional extensions.

Contribution

It provides the first example of homogeneous gradient solitons for the G$_2$-Laplacian flow, expanding understanding of soliton solutions in geometric flows.

Findings

First known homogeneous gradient soliton for G$_2$-Laplacian flow

Existence on spaces that are one-dimensional extensions

G$_2$-Laplacian flow admits such solitons

Abstract

In this note, we prove the existence of homogeneous gradient solitons for the G$_2$-Laplacian flow by providing the first known example of this type. This result singles out the G$_2$-Laplacian flow as the first known geometric flow admitting homogeneous gradient solitons on spaces that are one-dimensional extensions.