旋转里奇曲面

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-03-12 DOI:10.1007/s10231-024-01436-0

Iury Domingos, Roney Santos, Feliciano Vitório

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引用次数: 0

摘要

我们对三维欧几里得空间中高斯曲率 K 满足 $$\begin{aligned} 的旋转曲面进行分类。K\Delta K -\Vert \nabla K\Vert ^2-4K^3 = 0.作为应用，我们证明了有一个一参数族的此类曲面与单位欧几里得三球的边界正交。此外，我们还证明了这个族插值垂直大地线和临界天顶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Rotational Ricci surfaces

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Rotational Ricci surfaces

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature K satisfies

$$\begin{aligned} K\Delta K - \Vert \nabla K\Vert ^2-4K^3 = 0. \end{aligned}$$

These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.