### 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.

Original language | English |
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Pages (from-to) | 861-891 |

Journal | Advances in Mathematics |

State | Published - Nov 13 2017 |

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## Cite this

Tran, H. (2017). On closed manifolds with harmonic Weyl curvature.

*Advances in Mathematics*, 861-891.