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arXiv · 2602.07313

Manifolds with harmonic Weyl curvature and curvature operator of the second kind

Haiping Fu·Yao Lu
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Abstract

We prove that a compact Riemannian manifold of dimension $n\ge 8$ with harmonic Weyl curvature and $\frac{3(n-1)(n+2)}{4(3n-1)}$-nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. In particular, We also give a classification of four-dimensional manifolds with harmonic Weyl curvature satisfying a cone condition. This result generalizes the work in \cite{DFY24,FLD,Li22}.

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Haiping Fu, Yao Lu. 2026-02-07. Manifolds with harmonic Weyl curvature and curvature operator of the second kind. https://arxiv.org/abs/2602.07313

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