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New Curvature Operator of the Second Kind Conditions for Rigidity
We establish Tachibana-type rigidity theorems with the aid of the curvature operator of the second kind (COSK). A sharp estimate that combines the symmetric and commutator actions on Weyl tensors leads to a constant $C_{n}$, with $\frac{C_{n}}{n}\to\frac{5}{4}$, such that a complete Einstein manifol
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