{"title":"Ruled Ricci surfaces and curves of constant torsion","authors":"Alcides de Carvalho, Iury Domingos, Roney Santos","doi":"10.1007/s10455-025-09991-2","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 2","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-025-09991-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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