2020/11/19 by Shen, Xi Sisi
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2011.09683
We study an analogue of the Calabi flow in the non-Kähler setting for compact Hermitian manifolds with vanishing first Bott-Chern class. We prove a priori estimates for the evolving metric along the flow given a uniform bound on the Chern scalar curvature. If the Chern scalar curvature remains uniformly bounded for all time, we show that the flow converges smoothly to the unique Chern-Ricci-flat metric in the ∂∂-class of the initial metric.