127 citations · 350 across the 23 of their papers we have counts for
27 papers
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…
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…
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…
Holonomy restrictions from the curvature operator of the second kind
Jan Nienhaus, Peter Petersen, Matthias Wink +1
We show that an -dimensional Riemannian manifold with -nonnegative or -nonpositive curvature operator of the second kind has restricted holonomy or is flat. The re…
Betti numbers and the curvature operator of the second kind
Jan Nienhaus, Peter Petersen, Matthias Wink
We show that compact, -dimensional Riemannian manifolds with -nonnegative curvature operators of the second kind are either rational homology spheres or flat. Mor…
Tachibana-type Theorems and special Holonomy
Peter Petersen, Matthias Wink
We prove rigidity results for compact Riemannian manifolds in the spirit of Tachibana. For example, we observe that manifolds with divergence free Weyl tensors and $\lfloor \frac{n…