On Closed Manifolds with Harmonic Weyl Curvature

Abstract

We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key ingredients are new Bochner-Weitzenböck-Lichnerowicz type formulas for the Weyl tensor, which are generalizations of identities in dimension four.

27 pages, final version

References in corpus (2)

• The Weyl Tensor of Gradient Ricci Solitons
• On compact manifolds with harmonic curvature and positive scalar curvature

Cited by in corpus (6)

• Einstein four-manifolds of pinched sectional curvature
• Tachibana-type Theorems and special Holonomy
• New examples of compact Weyl-parallel manifolds
• The metric structure of compact rank-one ECS manifolds
• Four-manifolds of Pinched Sectional Curvature
• On compact Riemannian manifolds with harmonic weyl curvature