{"title":"Singularities of generic line congruences","authors":"M. Craizer, Ronaldo Garcia","doi":"10.2969/jmsj/88348834","DOIUrl":null,"url":null,"abstract":"Line congruences are 2-dimensional families of lines in 3space. The singularities that appear in generic line congruences are folds, cusps and swallowtails ([7]). In this paper we give a geometric description of these singularities. The main tool used is the existence of an equiaffine pair defining a generic line congruence. Mathematics Subject Classification (2010). 53A55, 57R45, 53A20.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Mathematical Society of Japan","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2969/jmsj/88348834","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Line congruences are 2-dimensional families of lines in 3space. The singularities that appear in generic line congruences are folds, cusps and swallowtails ([7]). In this paper we give a geometric description of these singularities. The main tool used is the existence of an equiaffine pair defining a generic line congruence. Mathematics Subject Classification (2010). 53A55, 57R45, 53A20.
期刊介绍：
The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).
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