Short-time behaviour of a modified Laplacian coflow of G2-structures

TL;DR

This paper introduces a modified Laplacian coflow for G2-structures, proving short-time existence and uniqueness of solutions, which advances understanding of geometric flows in special holonomy manifolds.

Contribution

It proposes a new parabolic modification of the Laplacian coflow for G2-structures and establishes foundational short-time existence and uniqueness results.

Findings

Modified flow is parabolic in the space of closed forms.

Proved short-time existence of solutions.

Proved uniqueness of solutions.

Abstract

We modify the Laplacian coflow of co-closed G2-structures - $\frac{d}{dt}\psi =\Delta \psi $ where $\psi $ is the closed dual 4-form of a $G_{2}$-structure $\varphi $. The modified flow is now parabolic in the direction of closed forms upto diffeomorphisms. We then prove short time existence and uniqueness of solutions to the modified flow.