Flows of $G_2$-Structures associated to Calabi-Yau Manifolds

Sébastien Picard; Caleb Suan

Flows of $G_2$-Structures associated to Calabi-Yau Manifolds

Differential Geometry 2023-06-07 v2 Analysis of PDEs

Authors: Sébastien Picard , Caleb Suan

Abstract

We establish a correspondence between a parabolic complex Monge-Amp\`ere equation and the $G_2$ -Laplacian flow for initial data produced from a K\"ahler metric on a complex $2$ - or $3$ -fold. By applying estimate for the complex Monge-Amp\`ere equation, we show that for this class of initial data the $G_2$ -Laplacian flow exists for all time and converges to a torsion-free $G_2$ -structure induced by a K\"ahler Ricci-flat metric. Similar results are obtained for the $G_2$ -Laplacian coflow, and in this case the coflow is related to the K\"ahler-Ricci flow.

Keywords

g2-structure laplacian flow calabi-yau manifold complex monge-ampere equation kahler-ricci flow torsion-free

Cite

@article{arxiv.2209.03411,
  title  = {Flows of $G_2$-Structures associated to Calabi-Yau Manifolds},
  author = {Sébastien Picard and Caleb Suan},
  journal= {arXiv preprint arXiv:2209.03411},
  year   = {2023}
}

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27 Pages; v2 (Minor Changes)

Flows of $G_2$-Structures associated to Calabi-Yau Manifolds

Abstract

Keywords

Cite

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