Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912421109563392 |
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| author | Earp, Henrique N. Sá Saavedra, Julieth Suan, Caleb |
| author_facet | Earp, Henrique N. Sá Saavedra, Julieth Suan, Caleb |
| contents | We explore three versions of the Laplacian coflow of $G_2$-structures on circle fibrations over Calabi--Yau 3-folds, interpreting their dimensional reductions to the Kähler geometry of the base. Precisely, we reduce Ansätze for the Laplacian coflow, modified or not by de Turck's trick, both on trivial products $CY^3\times S^1$ and on contact Calabi--Yau 7-manifolds, obtaining in each case a natural modification of the Kähler--Ricci flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds Earp, Henrique N. Sá Saavedra, Julieth Suan, Caleb Differential Geometry 53D10, 53E30, 53C25, 57R15 We explore three versions of the Laplacian coflow of $G_2$-structures on circle fibrations over Calabi--Yau 3-folds, interpreting their dimensional reductions to the Kähler geometry of the base. Precisely, we reduce Ansätze for the Laplacian coflow, modified or not by de Turck's trick, both on trivial products $CY^3\times S^1$ and on contact Calabi--Yau 7-manifolds, obtaining in each case a natural modification of the Kähler--Ricci flow. |
| title | Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds |
| topic | Differential Geometry 53D10, 53E30, 53C25, 57R15 |
| url | https://arxiv.org/abs/2406.15254 |