Flows of conformally coclosed $G_2$-structures with dilaton
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910120142700544 |
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| author | Karigiannis, Spiro Picard, Sébastien Suan, Caleb |
| author_facet | Karigiannis, Spiro Picard, Sébastien Suan, Caleb |
| contents | 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 Kähler--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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21055 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flows of conformally coclosed $G_2$-structures with dilaton Karigiannis, Spiro Picard, Sébastien Suan, Caleb Differential Geometry Analysis of PDEs 53E30, 53C25 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 Kähler--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. |
| title | Flows of conformally coclosed $G_2$-structures with dilaton |
| topic | Differential Geometry Analysis of PDEs 53E30, 53C25 |
| url | https://arxiv.org/abs/2511.21055 |