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Flows of Conformally Coclosed G 2 -Structures with Dilaton
Spiro Karigiannis1, Sébastien Picard2, Caleb Suan3
1Department of Pure Mathematics, University of Waterloo, Waterloo, ON Canada.
Journal of Geometric Analysis
|April 13, 2026
Summary
Geometric flows in G2-geometry are simplified through dimensional reduction, leading to new insights in complex geometry. This study introduces G2-Laplacian and anomaly flows, comparing their properties and existence.
Area of Science:
- Differential Geometry
- Geometric Analysis
- Mathematical Physics
Background:
- G2-structures are fundamental in various areas of geometry and physics.
- Dimensional reduction is a powerful technique for simplifying complex geometric problems.
- Understanding geometric flows is crucial for studying the evolution and properties of geometric structures.
Purpose of the Study:
- To explore the principle of dimensional reduction for G2-geometric flows.
- To introduce and analyze G2-Laplacian coflow and a G2-lift of the anomaly flow.
- To compare these G2 flows and investigate their short-time existence and fixed points.
Main Methods:
- Applying dimensional reduction to natural geometric flows in G2-geometry.
- Lifting the Kähler-Ricci flow to a G2-Laplacian coflow.
- Constructing a 7-dimensional lift of the anomaly flow on complex threefolds.
- Deforming conformally coclosed G2-structures using the G2-anomaly flow.
Main Results:
- Natural geometric flows in G2-geometry reduce to natural flows in complex geometry.
- The G2-Laplacian coflow is a lift of the Kähler-Ricci flow.
- The G2-anomaly flow deforms conformally coclosed G2-structures.
- Comparison between G2-anomaly flow and G2-Laplacian coflow is performed.
Conclusions:
- Dimensional reduction provides a systematic way to study G2-geometric flows.
- The introduced G2 flows offer new tools for investigating G2-geometry.
- Further research is needed on the short-time existence and fixed points of these flows.
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