{"title":"FOCAL SURFACES OF FRONTS ASSOCIATED TO UNBOUNDED PRINCIPAL CURVATURES","authors":"Keisuke Teramoto","doi":"10.1216/rmj.2023.53.1587","DOIUrl":null,"url":null,"abstract":"We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near nondegenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of singularities and geometrical properties of initial fronts. Moreover, we investigate behavior of the Gaussian curvature of the focal surface.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rocky Mountain Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/rmj.2023.53.1587","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: 0
Abstract
We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near nondegenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of singularities and geometrical properties of initial fronts. Moreover, we investigate behavior of the Gaussian curvature of the focal surface.
期刊介绍：
Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles.
The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics.
In addition, the journal publishes specialized conference proceedings.
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