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

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 ${\mathbb{HP}}^{m+1}\backslash \{\ast \}$. 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.

We added a new section giving a proof of the positivity of sectional curvatures for the constructed solitons for sufficiently small parameters. Corollary 1.8 has been strengthened to Theorem 1.8