30 citations · 101 across the 13 of their papers we have counts for
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A vanishing result for harmonic -forms
Matthias Wink
We prove that every primitive harmonic -form of a closed Kähler manifold of complex dimension vanishes provided its Kähler curvature operator is -po…
A Thorpe Trick for the Bochner Technique
Matthias Wink
We prove that for there exists such that every closed orientable Riemannian manifold with -posi…
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…
Vanishing theorems for Hodge numbers and the Calabi curvature operator
Kyle Broder, Jan Nienhaus, Peter Petersen +2
It is shown that a compact -dimensional Kähler manifold with -positive Calabi curvature operator has the rational cohomology of complex projective space. For even $…
New expanding Ricci solitons starting in dimension four
Jan Nienhaus, Matthias Wink
We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asy…
Einstein metrics on the Ten-Sphere
Jan Nienhaus, Matthias Wink
We prove the existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on the sphere Previously, the only even-dimensional spheres known…
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…
Estimation and Vanishing Results for Hodge numbers
Peter Petersen, Matthias Wink
We show that compact Kähler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the Kähler curvature…
The Bochner Technique and Weighted Curvatures
Peter Petersen, Matthias Wink
In this note we study the Bochner formula on smooth metric measure spaces. We introduce weighted curvature conditions that imply vanishing of all Betti numbers.
New Curvature Conditions for the Bochner Technique
Peter Petersen, Matthias Wink
We prove a vanishing and estimation theorem for the -Betti number of closed -dimensional Riemannian manifolds with a lower bound on the average of the lowest $n-p…
Complete Ricci solitons via estimates on the soliton potential
Matthias Wink
In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady…
Cohomogeneity one Ricci Solitons from Hopf Fibrations
Matthias Wink
This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit consists of two inequivalent -invariant irreducible summands,…