# Explicit Soliton for the Laplacian Co-Flow on a Solvmanifold

## TL;DR

This paper constructs an explicit soliton solution for the Laplacian co-flow of invariant G2-structures on a specific 7-dimensional solvmanifold, advancing understanding of geometric flows on homogeneous spaces.

## Contribution

It provides the first explicit soliton solution for the Laplacian co-flow on a particular almost Abelian 7-manifold, applying Lauret's Ansatz to homogeneous spaces.

## Key findings

- Explicit soliton solution found for the Laplacian co-flow on a solvmanifold.
- Demonstrates the applicability of Lauret's Ansatz to invariant G2-structures.
- Advances the study of geometric flows on homogeneous spaces.

## Abstract

We apply the general Ansatz in geometric flows on homogeneous spaces proposed by Jorge Lauret for the Laplacian co-flow of invariant $G_2$-structures on a Lie group, finding an explicit soliton on a particular almost Abelian $7$-manifold.