67 citations · 155 across the 26 of their papers we have counts for
31 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…
On the variational properties of the prescribed Ricci curvature functional
Artem Pulemotov, Wolfgang Ziller
We study the prescribed Ricci curvature problem for homogeneous metrics. Given a (0,2)-tensor field , this problem asks for solutions to the equation for so…
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…
The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups
Romina M. Arroyo, Artem Pulemotov, Wolfgang Ziller
We study the problem of prescribing the Ricci curvature in the class of naturally reductive metrics on a compact Lie group. We derive necessary as well as sufficient conditions for…
On the Ricci iteration for homogeneous metrics on spheres and projective spaces
Timothy Buttsworth, Artem Pulemotov, Yanir A. Rubinstein +1
We study the Ricci iteration for homogeneous metrics on spheres and complex projective spaces. Such metrics can be described in terms of modifying the canonical metric on the fiber…
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…