Ruled Ricci surfaces and curves of constant torsion

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-03-07 DOI:10.1007/s10455-025-09991-2

Alcides de Carvalho, Iury Domingos, Roney Santos

引用次数: 0

Abstract

We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the helicoid as the only surface of this kind that admits a parametrization with plane line of striction, and as the only with constant mean curvature.

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有规则的利玛窦曲面和恒定扭力曲线

我们证明了三维欧几里德空间中所有具有Ricci度量的不可展开直纹曲面都可以用常扭曲线及其二法线来构造。这使我们可以把螺旋面描述为这类曲面中唯一允许用平面约束线进行参数化的曲面，以及唯一具有恒定平均曲率的曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.