<p>We study flows of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-structures guided by the principle of dimensional reduction: natural geometric flows in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-geometry reduce to natural flows in complex geometry. Our main examples are the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-Laplacian coflow, which lifts the Kähler–Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-lift of the anomaly flow deforms conformally coclosed <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-structures. We compare the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-anomaly flow to the<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$G_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-Laplacian coflow, and investigate short-time existence and fixed points.</p>

Flows of Conformally Coclosed $G_2$-Structures with Dilaton

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2026年4月10日

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Spiro Karigiannis,
Sébastien Picard,
Caleb Suan

摘要

We study flows of $G_2$ $G_{2}$ -structures guided by the principle of dimensional reduction: natural geometric flows in $G_2$ $G_{2}$ -geometry reduce to natural flows in complex geometry. Our main examples are the $G_2$ $G_{2}$ -Laplacian coflow, which lifts the Kähler–Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The $G_2$ $G_{2}$ -lift of the anomaly flow deforms conformally coclosed $G_2$ $G_{2}$ -structures. We compare the $G_2$ $G_{2}$ -anomaly flow to the $G_2$ $G_{2}$ -Laplacian coflow, and investigate short-time existence and fixed points.

Flows of Conformally Coclosed \(G_2\)-Structures with Dilaton

摘要