Laplacian coflow for warped G₂-structures

2019/04/12 by Víctor Manero, Manero, Victor, Antonio Otal +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1904.06080

openalex publication_date 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Laplacian coflow of a G₂-structure on warped products of the form M⁷= M⁶ ×_f S¹ with M⁶ a compact 6-manifold endowed with an SU(3)-structure. We give an explicit reinterpretation of this flow as a set of evolution equations of the differential forms defining the SU(3)-structure on M⁶ 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 SU(3)-structure on M⁶ is nearly Kähler, symplectic half-flat or balanced.

Citations

• Existence, Convergence and Limit Map of the Laplacian Flow
• Laplacian Flow for Closed G₂-Structures: Short Time Behavior

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