Flows of conformally coclosed $G_2$-structures with dilaton

Spiro Karigiannis; Sébastien Picard; Caleb Suan

doi:10.1007/s12220-026-02416-x

Flows of conformally coclosed $G_2$-structures with dilaton

Differential Geometry 2026-04-14 v2 Analysis of PDEs

Authors: Spiro Karigiannis , Sébastien Picard , Caleb Suan

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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 K\"ahler--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.

Keywords

G2-structures conformally coclosed dilaton G2-Laplacian coflow anomaly flow dimensional reduction complex geometry short-time existence

Cite

@article{arxiv.2511.21055,
  title  = {Flows of conformally coclosed $G_2$-structures with dilaton},
  author = {Spiro Karigiannis and Sébastien Picard and Caleb Suan},
  journal= {arXiv preprint arXiv:2511.21055},
  year   = {2026}
}

Comments

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 $G_2$-structures with dilaton

Abstract

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