2005/03/28 by X. X. Chen, H. Li, Chen, X. X. +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #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.math/0503645
19 pages
arxiv created 2005/03/28 · openalex publication_date 2005/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was proved by H. Chen earlier that the property of the sum of any two eigenvalues of the curvature operator is positive is preserved under the ricci flow in all dimensional. By a recent result of Phong-Sturm, a similar notion of positive 2-traceless bisectional curvature positive is preserved on complex surface. We prove that this holds in all dimensional Kähler manifold. Moreover, the scalar curvature controls full curvature for this type of metrics.