Flows of conformally coclosed $G_2$-structures with dilaton

Spiro Karigiannis; SÃ©bastien Picard; Caleb Suan

doi:10.1007/s12220-026-02416-x

paper

Flows of conformally coclosed $G_{2}$ -structures with dilaton

arXiv:2511.21055 · doi:10.1007/s12220-026-02416-x

Abstract

We study flows of $G_{2}$ -structures guided by the principle of dimensional reduction: natural geometric flows in $G_{2}$ -geometry reduce to natural flows in complex geometry. Our main examples are the $G_{2}$ -Laplacian coflow, which lifts the KÃ¤hler--Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The $G_{2}$ -lift of the anomaly flow deforms conformally coclosed $G_{2}$ -structures. We compare the $G_{2}$ -anomaly flow to the $G_{2}$ -Laplacian coflow, and investigate short-time existence and fixed points.

35 pages, 2 tables. Version 2: Minor revisions and remarks added following referee's report. Final version, to appear in The Journal of Geometric Analysis

Flows of conformally coclosed G2​-structures with dilaton

Abstract

Flows of conformally coclosed $G_{2}$ -structures with dilaton