Manifolds with harmonic 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_ | 1866911430170640384 |
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| author | Fu, Haiping Lu, Yao Dai, Zhilin |
| author_facet | Fu, Haiping Lu, Yao Dai, Zhilin |
| contents | We prove that complete Riemannian manifolds of dimension $n\ge3$ with harmonic curvature and $\frac{n(n+2)}{2(n+1)}$-nonnegative curvature operator of the second kind must be Einstein. In particular, We show that complete Einstein manifolds of dimension $n\ge4$ with $\frac{3n(n-1)^2(n+2)}{2(5n^3+3n^2-30n+16)}$-nonnegative curvature operator of the second kind must be of constant curvature, which generalizes the work of Dai-Fu \cite{DF}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02722 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manifolds with harmonic curvature and curvature operator of the second kind Fu, Haiping Lu, Yao Dai, Zhilin Differential Geometry We prove that complete Riemannian manifolds of dimension $n\ge3$ with harmonic curvature and $\frac{n(n+2)}{2(n+1)}$-nonnegative curvature operator of the second kind must be Einstein. In particular, We show that complete Einstein manifolds of dimension $n\ge4$ with $\frac{3n(n-1)^2(n+2)}{2(5n^3+3n^2-30n+16)}$-nonnegative curvature operator of the second kind must be of constant curvature, which generalizes the work of Dai-Fu \cite{DF}. |
| title | Manifolds with harmonic curvature and curvature operator of the second kind |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.02722 |