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math.DG2026
New Curvature Operator of the Second Kind Conditions for Rigidity
Xiaolong Li, Peter Petersen
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…
math.DG2026
Tachibana's Theorem Revisited
Xiaolong Li, Peter Petersen
We prove Tachibana-type rigidity theorems for closed manifolds under weakened partial-sum conditions on the eigenvalues of curvature operators. Specifically, an Einstein manifold o…
math.DG2026
A characterization of complex projective space via the Calabi curvature operator
Hasan M. El-Hasan, Xiaolong Li, Jan Nienhaus +3
We prove a Tachibana-type result for Kähler-Einstein manifolds isolating complex projective space based on its Calabi curvature operator. The proof uses a new Bochner formula expre…