Leafwise flat forms on Inoue-Bombieri surfaces

Abstract

We prove that every Gauduchon metric on an Inoue-Bombieri surface admits a strongly leafwise flat form in its $\partial \overline{\partial }$-class. Using this result, we deduce uniform convergence of the normalized Chern-Ricci flow starting at any Gauduchon metric on all Inoue-Bombieri surfaces. We also show that the convergence is smooth with bounded curvature for initial metrics in the $\partial \overline{\partial }$-class of the Tricerri/Vaisman metric.

24 pages. Final version to appear in J. Funct. Anal

References in corpus (3)

• Almost Kähler Kodaira-Spencer problem
• The Chern-Ricci flow
• On the spectral sets of Inoue surfaces

Cited by in corpus (2)

• The Chern-Ricci flow
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs