{"title":"具有广义1型高斯映射的运河表面","authors":"J. Qian, Mengfei Su, Young Ho Kim","doi":"10.33044/REVUMA.1685","DOIUrl":null,"url":null,"abstract":"This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"17 1","pages":"199-211"},"PeriodicalIF":0.6000,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Canal surfaces with generalized 1-type Gauss map\",\"authors\":\"J. Qian, Mengfei Su, Young Ho Kim\",\"doi\":\"10.33044/REVUMA.1685\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.\",\"PeriodicalId\":54469,\"journal\":{\"name\":\"Revista De La Union Matematica Argentina\",\"volume\":\"17 1\",\"pages\":\"199-211\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista De La Union Matematica Argentina\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.33044/REVUMA.1685\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Union Matematica Argentina","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.33044/REVUMA.1685","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
This work considers a kind of classification of canal surfaces in terms of their Gauss map G in Euclidean 3-space. We introduce the notion of generalized 1-type Gauss map for a submanifold that satisfies ∆G = fG+gC, where ∆ is the Laplace operator, C is a constant vector, and (f, g) are non-zero smooth functions. First of all, we show that the Gauss map of any surface of revolution with unit speed profile curve in Euclidean 3-space is of generalized 1-type. At the same time, the canal surfaces with generalized 1-type Gauss map are discussed.
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Revista de la Unión Matemática Argentina is an open access journal, free of charge for both authors and readers. We publish original research articles in all areas of pure and applied mathematics.
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