We define a parabolic flow of almost Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. We show that the flow has a unique shorttime solution and also show a stability result when the background metric is quasi-Kähler with constant scalar curvature.
"A scalar Calabi-type flow in the almost Hermitian geometry." Tsukuba J. Math. 43 (1) 37 - 54, July 2019. https://doi.org/10.21099/tkbjm/1571968820