A flow of isometric $G_2$-structures. Short-time existence

Abstract

We introduce a flow of $G_2$-structures defining the same underlying Riemannian metric, whose stationary points are those structures with divergence-free torsion. We show short-time existence and uniqueness of the solution.

arXiv commentGeom Anal (2019)

References in corpus (7)

• The geometry of three-forms in six and seven dimensions
• Short-time behaviour of a modified Laplacian coflow of G2-structures
• Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds
• G2-structures and octonion bundles
• The spinorial energy functional on surfaces
• A spinorial energy functional: critical points and gradient flow
• A parabolic flow of balanced metrics

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• The Space of Closed $G_2$-Structures. I. Connections