Four-dimensional steady gradient Ricci solitons with 3-cylindrical tangent flows at infinity

Abstract

In this paper we consider 4-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed 4-manifold. In particular, we study the geometry at infinity of such Ricci solitons under the assumption that their tangent flow at infinity is the product of R with a 3-dimensional spherical space form. We also classify the tangent flows at infinity of 4-dimensional steady soliton singularity models in general.