On compact Riemannian manifolds with harmonic weyl curvature

2018/10/15 by Fu, Haiping, He, Huiya
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06301

Abstract

We give some rigidity theorems for an n(≥4)-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant σ₂. Moreover, when n=4, we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant σ₂ is isometric to a quotient of the round \mathbbS⁴.

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