2016/09/22 by Bing-Long Chen, Chen, Bing-Long, Xiaokui Yang +1 · 3 citations
Mathematics · #53C55 #Combinatorics #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Geology #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Holomorphic function #Kähler manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Pure mathematics #Ricci-flat manifold #Scalar curvature #Sectional curvature #Symplectic geometry #Topology (electrical circuits) #Type (biology) #math.DG #msc:53C55
paper · pdf · doi:10.48550/arxiv.1609.06918
12 pages, to appear in Math. Ann
openalex publication_date 2016/09/22 · openalex created_date 2016/10/07 · arxiv created 2017/11/09 · arxiv updated 2017/11/10 · openalex updated_date 2026/07/28
In this paper, we show that any compact Kähler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a Kähler-Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold X homotopic to a compact Riemannian manifold with negative sectional curvature, for any almost complex structure J compatible with the symplectic form, there is no non-constant J-holomorphic entire curve f:C → X.