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arXiv · 1904.06080

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

Victor Manero·Antonio Otal·Raquel Villacampa
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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 K\"ahler, symplectic half-flat or balanced.

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Victor Manero, Antonio Otal, Raquel Villacampa. 2019-04-12. Laplacian coflow for warped $\mathrm{G}_2$-structures. https://arxiv.org/abs/1904.06080

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