Spherical Ricci tori with rotational symmetry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915711140495360 |
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| author | Domingos, Iury Onnis, Irene. I. |
| author_facet | Domingos, Iury Onnis, Irene. I. |
| contents | In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*}
(K - c)ΔK - |\nabla K|^2 - 4K(K - c)^2 = 0, \end{equation*} for some $c>0$. We explicitly construct a two-parameter family of such metrics with rotational symmetry and show that infinitely many non-isometric examples can be realized on the same torus. Moreover, we investigate their realization as induced metrics on compact rotational surfaces in $\mathbb{S}^3$, establishing the existence of embedded compact spherical Ricci surfaces by controlling a period function associated with the isometric immersion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03096 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spherical Ricci tori with rotational symmetry Domingos, Iury Onnis, Irene. I. Differential Geometry 53C42, 53C40 In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*} (K - c)ΔK - |\nabla K|^2 - 4K(K - c)^2 = 0, \end{equation*} for some $c>0$. We explicitly construct a two-parameter family of such metrics with rotational symmetry and show that infinitely many non-isometric examples can be realized on the same torus. Moreover, we investigate their realization as induced metrics on compact rotational surfaces in $\mathbb{S}^3$, establishing the existence of embedded compact spherical Ricci surfaces by controlling a period function associated with the isometric immersion. |
| title | Spherical Ricci tori with rotational symmetry |
| topic | Differential Geometry 53C42, 53C40 |
| url | https://arxiv.org/abs/2601.03096 |