On closed manifolds with harmonic Weyl curvature

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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 languageEnglish
Pages (from-to)861-891
Number of pages31
JournalAdvances in Mathematics
StatePublished - Dec 15 2017


  • Bochner formula
  • Harmonic Weyl curvature
  • Tachibana's theorem


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