Modified Laplacian coflow of G2-structures on manifolds with symmetry

We consider G2G2-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 G2G2-structures are determined by their torsion components. We then study the modified Laplacian coflow dψdt=Δψψ+2d((C−TrT)φ) of these G2G2-structures, where φ and ψ   are the fundamental 3-form and 4-form which define the G2G2-structure and ΔψΔψ is the Hodge Laplacian associated with the G2G2-structure. This flow is known to have short-time existence and uniqueness. We analyze the soliton equations for this flow and obtain new compact soliton solutions.