The transverse Chern-Ricci flow

2015/06/08 by Hong Huang, Huang, Hong
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1506.02542

preliminary version

arxiv created 2015/06/08 · openalex publication_date 2015/06/08 · arxiv updated 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce transverse Chern-Ricci flow for transversely Hermitian foliations, which is analogous to the Chern-Ricci flow. We show that when F is homologically orientable and the basic first Bott-Chern class is zero, starting at any transversely Hermitian metric the flow exists for all time and as t→ ∞ converges smoothly to a transversely Hermitian metric ω_∞ with the transverse Chern-Ricci form ρ^T(ω_∞)=0. We also determine the maximal existence time of the flow in the general case. These are foliated version of results of Gill and Tosatti-Weinkove, and also extend recent work of Bedulli-He-Vezzoni.

Citations

• Sasaki manifolds with positive transverse orthogonal bisectional curvature

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