Paper · Mar 19, 2025
Cohomogeneity one 4-dimensional gradient Ricci solitons
As on arXiv
Abstract
Simply-connected four-dimensional gradient Ricci solitons that are invariant under a compact cohomogeneity one group action have been studied extensively. However, the special case where the group is (the smallest possible example) has received comparatively little attention. The purpose of this article is to give a comprehensive study of simply-connected -invariant expanding and shrinking cohomogeneity one gradient Ricci solitons. The first result is the construction of new 3-parameter families of complete -invariant asymptotically conical expanding gradient Ricci solitons. New shrinking Kähler -invariant gradient Ricci solitons in dimension 4 with orbifold singularities are also constructed, leading to a classification of such metrics when the base space of the orbifold is a simply-connected smooth manifold. Finally, we highlight numerical evidence that all the compact cohomogeneity one shrinking gradient Ricci solitons are known.
- Submitted
- Mar 19, 2025
- Subjects
- math.DG
Comments: 52 pages, 6 figures
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