Manifolds with harmonic Weyl curvature and curvature operator of the second kind
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910015209603072 |
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| author | Fu, Haiping Lu, Yao |
| author_facet | Fu, Haiping Lu, Yao |
| contents | 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}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_07313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manifolds with harmonic Weyl curvature and curvature operator of the second kind Fu, Haiping Lu, Yao Differential Geometry 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}. |
| title | Manifolds with harmonic Weyl curvature and curvature operator of the second kind |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2602.07313 |