<p>We establish the existence of two 3-parameter families of non-Einstein, non-shrinking Ricci solitons: one on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb {H}^{m+1}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> and one on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb{H}\mathbb{P}^{m+1}\backslash \{*\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">H</mi> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo stretchy="true">\</mo> <mrow> <mo stretchy="false">{</mo> <mrow /> <mo>∗</mo> <mo stretchy="false">}</mo> </mrow> </mrow> </mrow> </math></EquationSource> </InlineEquation>. 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathbb {O}^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">O</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>, which contains a 1-parameter subfamily of asymptotically paraboloidal steady Ricci solitons based on the Bourguignon–Karcher sphere.</p>

Non-Shrinking Ricci Solitons of Cohomogeneity One from the Quaternionic Hopf Fibration

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发表日期：

2026年3月19日

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Hanci Chi

摘要

We establish the existence of two 3-parameter families of non-Einstein, non-shrinking Ricci solitons: one on $\mathbb {H}^{m+1}$ $H^{m + 1}$ and one on $\mathbb{H}\mathbb{P}^{m+1}\backslash \{*\}$ $H P^{m + 1} \ {*}$ . 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 $\mathbb {O}^2$ $O^{2}$ , which contains a 1-parameter subfamily of asymptotically paraboloidal steady Ricci solitons based on the Bourguignon–Karcher sphere.