2007/01/25 by Jianguo Cao, Cao, Jianguo
Mathematics · #53C99 #58C99 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C99 #msc:58C99
paper · pdf · doi:10.48550/arxiv.math/0701742
openalex publication_date 2007/01/25 · arxiv created 2007/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study certain compact 4-manifolds with non-negative sectional curvature K. If s is the scalar curvature and W+ is the self-dual part of Weyl tensor, then it will be shown that there is no metric g on S2 × S2 with both (i) K > 0 and (ii) 1/6 s - W+ ≥ 0. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a theorem of Hamilton: ``If a simply-connected, closed 4-manifold M4 admits a metric g of non-negative curvature operator, then M4 is one of S4, \Bbb CP2 and S2 × S2". Our method is different from Hamilton's and is much simpler. A new version of the second variational formula for minimal surfaces in 4-manifolds is proved.