A generalized Frankel conjecture via the Yang-Mills flow

2025/11/06 by Jiangtao Li, Li, Jiangtao
Mathematics · #32Q15 #32Q30 #53C07 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.04003

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

In this note, we introduce a new curvature condition called the 2-positive bisectional curvature on compact Kähler manifolds. We then deduce a characterization theorem for manifolds with 2-positive bisectional curvature, which can be regarded as a variant of the classical Frankel conjecture (cf.\citeFra61,SY80) and its generalizations (cf.\citeSiu80,Mok88).

Citations

• An Extension of Mok's Theorem on the Generalized Frankel Conjecture
• Manifolds with 1/4-pinched Curvature are Space Forms
• On Kähler manifolds with positive orthogonal bisectional curvature
• Manifolds with positive curvature operators are space forms
• Sharp Dimension Estimates of Holomorphic Functions and Rigidity

Related

• On Kähler manifolds with positive orthogonal bisectional curvature
• Frankel Conjecture and Sasaki geometry
• The generalized Frankel conjecture in Sasaki geometry
• A note on Kähler-Ricci soliton
• The Kähler-Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator