15 citations · 29 across the 8 of their papers we have counts for
10 papers · 1 filter
The Hopf conjecture with -symmetry
Jan Nienhaus, Dennis Wulle
We prove that any closed even-dimensional manifold with positive sectional curvature admitting an isometric action by a 3-torus has positive Euler characteristic. We also prove the…
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…
Fixed Point Homogeneous Orbifolds with Positive Sectional Curvature
Jan Nienhaus, Dennis Wulle
We classify fixed point homogeneous Riemannian orbifolds with positive sectional curvature up to equivariant diffeomorphism. As a corollary we obtain a classification of positively…
On Hopf's conjecture and positive second intermediate Ricci curvature
Lee Kennard, Lawrence Mouillé, Jan Nienhaus
Hopf conjectured that even-dimensional closed Riemannian manifolds with positive sectional curvature have positive Euler characteristic. The conclusion of the conjecture is known t…
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…
An improved four-periodicity theorem and a conjecture of Hopf with symmetry
Jan Nienhaus
In the 1930s, H. Hopf conjectured that a closed, even-dimensional manifold of positive sectional curvature has positive Euler characteristic. We show this under the additional assu…
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…