{"title":"Approximations of Singular Surfaces with Standard Cuspidal Edges","authors":"Kentaro Saji, Yoshiki Yamamoto","doi":"10.1556/012.2023.04301","DOIUrl":null,"url":null,"abstract":"We consider a function from the Euclidean three space whose zero set is the image of the standard cuspidal edge. The composition of a parametrized singular surface in the three space with this function provides an approximation of the surface by the standard cuspidal edge. Taking a look at singularities of this composition, we study various approximations of singular surfaces like the cross cap, the generalized cuspidal edge and the swallowtail by standard cuspidal edges.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2023.04301","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We consider a function from the Euclidean three space whose zero set is the image of the standard cuspidal edge. The composition of a parametrized singular surface in the three space with this function provides an approximation of the surface by the standard cuspidal edge. Taking a look at singularities of this composition, we study various approximations of singular surfaces like the cross cap, the generalized cuspidal edge and the swallowtail by standard cuspidal edges.
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