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arXiv · 1709.02149

Cohomogeneity-one $G_2$-Laplacian flow on 7-torus

Hongnian Huang·Yuanqi Wang·Chengjian Yao
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Abstract

We prove the hypersymplectic flow of simple type on standard torus $\mathbb{T}^4$ exists for all time and converges to the standard flat structure modulo diffeomorphisms. This result in particular gives the first example of a cohomogeneity-one $G_2$-Laplacian flow on a compact $7$-manifold which exists for all time and converges to a torsion-free $G_2$ structure modulo diffeomorphisms.

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Hongnian Huang, Yuanqi Wang, Chengjian Yao. 2020-02-03. Cohomogeneity-one $G_2$-Laplacian flow on 7-torus. https://doi.org/10.1112/jlms.12137

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