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

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 different...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Authors: Manero, Victor, Otal, Antonio, Villacampa, Raquel
Format: Article
Language:English
Subjects:
Differential equations
Online Access:Get full text
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Summary: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.
ISSN:2331-8422