Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms

2014/09/12 by Yuxin Dong, Chong, Tian, Dong, Yuxin +4
Mathematics · Physics and Astronomy · #53C21 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 53C20

paper · pdf · doi:10.48550/arxiv.1409.3703

openalex publication_date 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some L^p and L^∞ pinching results are established to characterize Kähler-Einstein manifolds among Kähler manifolds with constant scalar curvature, and others are given to characterize complex space forms among Kähler-Einstein manifolds. Finally, these pinching results may be combined to characterize complex space forms among Kähler manifolds with constant scalar curvature.

Citations

• Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature

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