Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds

We explore three versions of the Laplacian coflow of $G_2$-structures on circle fibrations over Calabi–Yau 3-folds, interpreting their dimensional reductions to the Kähler geometry of the base. Precisely, we reduce Ansätze for the Laplacian coflow, modified or not by de Turck’s trick, both on trivial products $C{Y}^3\times S^1$ and on contact Calabi–Yau 7-manifolds, obtaining in each case a natural modification of the Kähler–Ricci flow.