Spherical Ricci tori with rotational symmetry

Iury Domingos; Irene. I. Onnis

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arXiv · 2601.03096

Spherical Ricci tori with rotational symmetry

Iury Domingos·Irene. I. Onnis

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Abstract

In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*} (K - c)\Delta K - |\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.

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BibTeX RIS

Iury Domingos, Irene. I. Onnis. 2026-01-06. Spherical Ricci tori with rotational symmetry. https://arxiv.org/abs/2601.03096

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