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arXiv · 2601.02722

Manifolds with harmonic curvature and curvature operator of the second kind

Haiping Fu·Yao Lu·Zhilin Dai
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Abstract

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}.

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Haiping Fu, Yao Lu, Zhilin Dai. 2026-01-06. Manifolds with harmonic curvature and curvature operator of the second kind. https://arxiv.org/abs/2601.02722

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