Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration

TL;DR

This paper constructs new families of non-shrinking Ricci solitons with cohomogeneity one, based on quaternionic and octonionic Hopf fibrations, including asymptotically paraboloidal steady solitons.

Contribution

It introduces multiple parameter families of non-Einstein, non-shrinking Ricci solitons on quaternionic and octonionic spaces, expanding known solutions with new geometric structures.

Findings

Existence of two 3-parameter families on quaternionic spaces.

Presence of a 2-parameter family on octonionic space.

Identification of asymptotically paraboloidal steady Ricci solitons.

Abstract

We establish the existence of two 3-parameter families of non-Einstein, non-shrinking Ricci solitons: one on $\mathbb{H}^{m+1}$ and one on $\mathbb{HP}^{m+1}\backslash\{*\}$. Each family includes a continuous 1-parameter subfamily of asymptotically paraboloidal (non-collapsed) steady Ricci solitons, with the Jensen sphere as the base. Additionally, we extend this result by proving the existence of a 2-parameter family on $\mathbb{O}^2$, which contains a 1-parameter subfamily of asymptotically paraboloidal steady Ricci solitons based on the Bourguignon--Karcher sphere.