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arXiv · 2406.15254

Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds

Henrique N. Sá Earp·Julieth Saavedra·Caleb Suan
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Abstract

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 K\"ahler geometry of the base. Precisely, we reduce Ans\"atze 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 K\"ahler--Ricci flow.

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Henrique N. Sá Earp, Julieth Saavedra, Caleb Suan. 2024-06-21. Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds. https://arxiv.org/abs/2406.15254

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