Manifolds with positive curvature operator are space form, preprint (2009)
Christoph Böhm, Burkhard Wilking
that a compact three-manifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In dimension four Hamilton showed that compact four-manifolds with positive...
Manifolds with 1/4-pinched flag curvature (2009)
We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We...
NON-NEGATIVE CURVATURE OBSTRUCTIONS IN COHOMOGENEITY ONE AND THE KERVAIRE SPHERES (2008)
Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller
Most examples of manifolds with non-negative sectional curvature are obtained via product and quotient constructions, starting from compact Lie groups with bi-invariant metrics. In [GZ1] a new large...
Positively curved cohomogeneity one manifolds and 3-Sasakian geometry (2008)
Karsten Grove, Burkhard Wilking, Wolfgang Ziller
Abstract. We provide an exhaustive description of all simply connected positively curved cohomogeneity one manifolds. The description yields a complete classification in all dimensions but 7, where...
Nonnegatively and Positively curved manifolds (2007)
This is a survey written for a special edition of the journal of differential geometry.
Manifolds with positive curvature operators are space forms (2006)
Boehm, Christoph, Wilking, Burkhard
We confirm a conjecture of Hamilton: On compact manifolds the normalized Ricci flow evolves metrics with positive curvature operators to limit metrics with constant curvature.
A duality theorem for Riemannian foliations in nonnegative sectional curvature (2006)
Using a new type of Jacobi field estimate we will prove a duality theorem for singular Riemannian foliations in complete manifolds of nonnegative sectional curvature.
Positively curved manifolds with symmetry (2006)
There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above $24$ all known examples are diffeomorphic to locally rank one symmetric...
Positively curved manifolds with symmetry (2006)
There are very few examples of Riemannian manifolds with positive sectionalcurvature known. In fact in dimensions above 24 all known examplesare diffeomorphic to locally rank one symmetric spaces. We...
Spherical rank rigidity and Blaschke manifolds (2003)
Shankar, Krishnan, Spatzier, Ralf, Wilking, Burkhard
Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate point at t=\pi. The...
Group actions on manifolds of nonnegative curvature and generalized Bieberbach theorems / (1998)
Münster (Westfalen), University, Diss, 1998 (Nur beschränkt für den Austausch).