The Laplacian coflow on almost-abelian Lie groups

TL;DR

This paper explicitly solves the Laplacian coflow of G_2-structures on seven-dimensional almost-abelian Lie groups, introduces new soliton examples, and discusses solutions with finite existence intervals.

Contribution

It provides explicit solutions, constructs novel non-eigenform solitons, and analyzes solutions with bounded existence intervals for the Laplacian coflow.

Findings

Explicit solutions of the Laplacian coflow on almost-abelian Lie groups

New examples of non-eigenform solitons

Existence of solutions with finite time intervals

Abstract

We find explicit solutions of the Laplacian coflow of $G_2-$structures on seven-dimensional almost-abelian Lie groups. Moreover, we construct new examples of solitons for the Laplacian coflow which are not eigenforms of the Laplacian and we exhibit a solution, which is not a soliton, having a bounded interval of existence.