3 papers
math.DG2025
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…
math.DG2025
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 $…
math.DG2022
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…