Short-time behaviour of a modified Laplacian coflow of G2-structures

Abstract

We modify the Laplacian coflow of co-closed G2-structures - $\frac{d}{dt}\psi =\Delta \psi$ where $\psi$ is the closed dual 4-form of a $G_2$-structure $\phi$. The modified flow is now parabolic in the direction of closed forms upto diffeomorphisms. We then prove short time existence and uniqueness of solutions to the modified flow.

39 pages, fixed typos, expanded published version

References in corpus (13)

• Ricci Flow and the Poincare Conjecture
• The geometry of three-forms in six and seven dimensions
• Flows of G_2 Structures, I
• Deformations of G_2 and Spin(7) Structures on Manifolds
• Soliton solutions for the Laplacian coflow of some $G_2$-structures with symmetry
• Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior
• Some remarks on G_2-structures
• Moduli spaces of G2 manifolds
• Local geometry of the G2 moduli space
• Existence, Convergence and Limit Map of the Laplacian Flow
• Conformal equivalence between certain geometries in dimension 6 and 7
• Energy functionals and soliton equations for G_2-forms
• G2-structure deformations and warped products

Cited by in corpus (23)

• Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness
• New invariants of G_2-structures
• Laplacian flow of homogeneous G2-structures and its solitons
• G2-structures and octonion bundles
• Shi-type estimates and finite time singularities of flows of G${}_2$ structures
• Foliated eight-manifolds for M-theory compactification
• A parabolic flow of balanced metrics
• Harmonic flow of geometric structures
• A gradient flow of isometric ${\mathrm{G}}_2$ structures
• Estimates and monotonicity for a heat flow of isometric G2-structures
• A flow of isometric $G_2$-structures. Short-time existence
• Modified Laplacian coflow of $G_2$-structures on manifolds with symmetry
• Flows of ${\mathrm{G}}_2$-structures on contact Calabi--Yau $7$-manifolds
• Geometric Flows of $G_2$-Structures on 3-Sasakian 7-Manifolds
• Explicit Soliton for the Laplacian Co-Flow on a Solvmanifold
• Foliated backgrounds for M-theory compactifications (I)
• Foliated backgrounds for M-theory compactifications (II)
• Curvature pinching estimate under the Laplacian G_{2} flow
• On $G_2$-structures, special metrics and related flows
• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion
• Invariant cocalibrated $G_2$-structures on nilmanifolds
• Real analyticity of the modified Laplacian coflow
• A remark on the Laplacian flow and the modified Laplacian co-flow in G2-Geometry