On compact manifolds with harmonic curvature and positive scalar curvature

Abstract

Let $M^n(n\ge 3)$ be an $n$-dimensional compact Riemannian manifold with harmonic curvature and positive scalar curvature. Assume that $M^n$ satisfies some integral pinching conditions. We give some rigidity theorems on compact manifolds with harmonic curvature and positive scalar curvature. In particular, Theorem 1.4, Corollary 1.6 and Theorem 1.9 are sharp for our conditions have the additional properties of being sharp. By this we mean that we can precisely characterize the case of equality.

arXiv admin note: text overlap with arXiv:1408.0902 by other authors. We revise the old version, and add some content. text overlap with arXiv:1511.07094

References in corpus (3)

• Fourth order curvature flows and geometric applications
• Rigidity Theorem for integral pinched shrinking Ricci solitons
• On conformally flat manifolds with constant positive scalar curvature

Cited by in corpus (1)

• On Closed Manifolds with Harmonic Weyl Curvature