Laplacian coflow for warped ${\mathrm{G}}_2$-structures

Abstract

We consider the Laplacian coflow of a ${\mathrm{G}}_2$-structure on warped products of the form $M^7=M^6{\times }_f{S}^1$ with $M^6$ a compact 6-manifold endowed with an $\mathrm{SU}(3)$-structure. We give an explicit reinterpretation of this flow as a set of evolution equations of the differential forms defining the $\mathrm{SU}(3)$-structure on $M^6$ and the warping function $f$. Necessary and sufficient conditions for the existence of solution for this flow are given. Finally we describe new long time solutions for this flow where the $\mathrm{SU}(3)$-structure on $M^6$ is nearly Kähler, symplectic half-flat or balanced.

References in corpus (3)

• Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior
• Einstein warped G2 and Spin(7) manifolds
• Geometric Flows of G_2 Structures