18 citations · 45 across the 7 of their papers we have counts for
10 papers
Initial value problems on cohomogeneity one manifolds, I
Luigi Verdiani, Wolfgang Ziller
We study initial value problems for various geometric equations on a cohomogeneity manifold near a singular orbit. We show that when prescribing the Ricci curvature, or finding sol…
Curvature homogeneous manifolds in dimension 4
Luigi Verdiani, Wolfgang Ziller
We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either…
Smoothness Conditions in Cohomogeneity manifolds
Luigi Verdiani, Wolfgang Ziller
In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Alo…
Seven dimensional cohomogeneity one manifolds with nonnegative curvature
Luigi Verdiani, Wolfgang Ziller
We show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature, unless it admits one with positive curvature. As…
Concavity and rigidity in non-negative curvature
Luigi Verdiani, Wolfgang Ziller
This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-neg…
A positively curved manifold homeomorphic to TS
Karsten Grove, Luigi Verdiani, Wolfgang Ziller
We construct a new 7-dimensional manifold with positive sectional curvature which is 2-connected with π_3=\Z_2 and admits an isometric group action with one dimensional quotient.