Harmonic 2-forms and positively curved 4-manifolds

2019/08/31 by Liu, Kefeng, Wan, Jianming
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1909.00110

Abstract

We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a Kato type inequality, then it is definite. We also discuss some new insights for compact Riemannian 4-manifolds of positive sectional curvature.

Related

• Four-manifolds with positive curvature
• 4-dimensional Riemannian manifolds with a harmonic 2-form of constant length
• Riemannian Manifolds with positive sectional curvature
• Compact 4-manifolds with harmonic Weyl tensor and nonnegative biorthogonal curvature
• 4-dimensional compact manifolds with nonnegative biorthogonal curvature