Non-negatively Curved Cohomogeneity One Manifolds Chenxu He Prof. Wolfgang Ziller, Advisor A Riemannian manifold M is called cohomogeneity one if it admits an isometric action by a compact Lie group G and the orbit space is one dimension. Many new examples of non-negatively curved manifolds were discovered recently in this category. However not every cohomogeneity one manifold carries an invari...

We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the main result in [12] to show that there are no noncompact cohomogeneity one s...