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arXiv · 2011.11168

Iterated collapsing phenomenon on $G_2$-manifolds

Yang Li
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Abstract

We propose a new collapsing mechanism for $G_2$-metrics, with the generic region admitting a circle bundle structure over a K3 fibration over a Riemann surface. The adiabatic description involves a weighted version of the maximal submanifold equation. In a local smooth setting we prove the existence of formal power series solutions, and the problem of compactification is discussed at a heuristic level. The $Spin(7)$ analogue is also discussed.

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Yang Li. 2020-11-23. Iterated collapsing phenomenon on $G_2$-manifolds. https://arxiv.org/abs/2011.11168

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