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math.DG2026

Some vanishing theorems on double form and curvature operator of the second kind

Hai-Ping Fu, Yao Lu

We establish a Bochner formula for double forms in terms of the curvature operator of the second kind. As an application, we prove that a complete Riemannian manifold of dimension…

math.DG2026

K{ä}hler Einstein manifolds and the Calabi curvature operator

Zhi-Lin Dai, Hai-Ping Fu, Yao Lu

In this paper, we study the Calabi curvature operator on K{ä}hler manifolds. First, we prove that if the Calabi curvature operator on K{ä}hler manifolds satisfies $\frac{n\left(n +…

math.DG2026

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

Haiping Fu, Yao Lu

We prove that a compact Riemannian manifold of dimension with harmonic Weyl curvature and -nonnegative curvature operator of the second kind i…

math.DG2026

Manifolds with harmonic curvature and curvature operator of the second kind

Haiping Fu, Yao Lu, Zhilin Dai

We prove that complete Riemannian manifolds of dimension with harmonic curvature and -nonnegative curvature operator of the second kind must be Einst…

math.DG2025

New rigidity theorem of Einstein manifolds and curvature operator of the second kind

Haiping Fu, Yao Lu

Using Bochner techniques, we prove that a compact Einstein manifold of dimension has constant curvature provided that the curvature operator of the second kind satisfies…