Modified Laplacian coflow of $G_2$-structures on manifolds with symmetry

Abstract

We consider $G_2$-structures on $7$-manifolds that are warped products of an interval and a six-manifold, which is either a Calabi-Yau manifold, or a nearly Kähler manifold. We show that in these cases the $G_2$-structures are determined by their torsion components up to a phase factor. We then study the modified Laplacian coflow $\frac{d\psi }{dt}={\Delta }_{\psi }\psi +2d\left(\left(C-TrT\right)\phi \right)$ of these $G_2$-structures, where $\phi$ and $\psi$ are the fundamental $3$-form and $4$-form which define the $G_2$-structure and ${\Delta }_{\psi }$ is the Hodge Laplacian associated with the $G_2$-structure. This flow is known to have short-time existence and uniqueness. We analyse the soliton equations for this flow and obtain new compact soliton solutions.

36 pages, 3 figures

References in corpus (1)

• Curvature decomposition of G_2 manifolds

Cited by in corpus (4)

• Laplacian flow of homogeneous G2-structures and its solitons
• Estimates and monotonicity for a heat flow of isometric G2-structures
• Curvature pinching estimate under the Laplacian G_{2} flow
• Real analyticity of the modified Laplacian coflow