Flows of G₂-Structures associated to Calabi-Yau Manifolds

2022/09/07 by Picard, Sébastien, Suan, Caleb · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.03411

Abstract

We establish a correspondence between a parabolic complex Monge-Ampère equation and the G₂-Laplacian flow for initial data produced from a Kähler metric on a complex 2- or 3-fold. By applying estimate for the complex Monge-Ampère equation, we show that for this class of initial data the G₂-Laplacian flow exists for all time and converges to a torsion-free G₂-structure induced by a Kähler Ricci-flat metric. Similar results are obtained for the G₂-Laplacian coflow, and in this case the coflow is related to the Kähler-Ricci flow.

Cited by

• Flows of conformally coclosed G₂-structures with dilaton

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