Paper · Oct 16, 2025
Cohomogeneity One Expanding Ricci Solitons and the Expander Degree
As on arXiv
Abstract
We consider the space of smooth gradient expanding Ricci soliton structures on and which are invariant under the action of . In the case of each topology, there exists a -parameter family of cohomogeneity one solitons asymptotic to cones over the link , as constructed by Nienhaus-Wink and Buzano-Dancer-Gallaugher-Wang. By analyzing the resultant soliton ODEs, we reconstruct the -parameter families in each case and provide an alternate proof of conicality. Analogous to work of Bamler and Chen, we define a notion of expander degree for these cohomogeneity one solitons through a properness result. We then proceed to calculate this cohomogeneity one expander degree in the cases of the specific topologies.
- Submitted
- Oct 16, 2025
- Last revised
- Oct 22, 2025 (v2)
- Subjects
- math.DG
Comments: Attributed credit more appropriately, clarified main results, fixed citations and rendering
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
On steady and expanding Ricci solitons with asymptotic symmetries
Topics Homogeneous spaces, Ricci solitons · Shared terms “expanding Ricci”
-
Inhomogeneous deformations of Einstein solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Shared terms “parameter family”, “cohomogeneity”
-
Classification of superpotentials for cohomogeneity one Ricci solitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “specific”
-
Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “parameter family”
-
Ricci solitons as submanifolds of complex hyperbolic spaces
Topics Homogeneous spaces, Ricci solitons · Shared terms “expanding Ricci”
-
Expanding Ricci solitons and Higgs bundles
Topics Homogeneous spaces, Ricci solitons · Shared terms “expanding Ricci”
-
On Ricci Solitons with Isoparametric Potential Functions
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”
-
Cohomogeneity one 4-dimensional gradient Ricci solitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “parameter family”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11A.13Homogeneous Flows
A computable laboratory: the flow on Thurston’s geometries.
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.