{"title":"Homothetic $$\\alpha $$ -Self-Similar Solutions to the Mean Curvature Flow in Minkowski 3-Space","authors":"Ajay Kumar Yadav, Akhilesh Yadav","doi":"10.1007/s00574-024-00413-8","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we classify the non-degenerate ruled surfaces which are homothetic <span>\\(\\alpha \\)</span>-self-similar solutions to the mean curvature flow (MCF) in Minkowski 3-space <span>\\(\\mathbb {E}^3_1\\)</span>. Other than cylindrical surfaces as in <span>\\(\\mathbb {E}^3\\)</span>, we find a class of non-cylindrical ruled surface with null rulings, in particular, the null scrolls. Further, we investigate the non-degenerate surfaces of revolutions generated by non-null curve as homothetic <span>\\(\\alpha \\)</span>-self-similar solutions to the MCF according to the causality of their rotation axes as spacelike, timelike and lightlike.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"37 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Brazilian Mathematical Society, New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00574-024-00413-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we classify the non-degenerate ruled surfaces which are homothetic \(\alpha \)-self-similar solutions to the mean curvature flow (MCF) in Minkowski 3-space \(\mathbb {E}^3_1\). Other than cylindrical surfaces as in \(\mathbb {E}^3\), we find a class of non-cylindrical ruled surface with null rulings, in particular, the null scrolls. Further, we investigate the non-degenerate surfaces of revolutions generated by non-null curve as homothetic \(\alpha \)-self-similar solutions to the MCF according to the causality of their rotation axes as spacelike, timelike and lightlike.
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