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arXiv · 1602.01429

On Closed Manifolds with Harmonic Weyl Curvature

Hung Tran
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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.

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Hung Tran. 2017-11-14. On Closed Manifolds with Harmonic Weyl Curvature. https://doi.org/10.1016/j.aim.2017.10.030

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