{"title":"正规和正切子流形的一些几何性质","authors":"Josué Meléndez, Eduardo Rodríguez-Romero","doi":"10.1016/j.difgeo.2023.102063","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we study some special ruled surfaces in a 3-dimensional Riemannian manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>. Given an immersed surface <em>M</em> into <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>, we consider the ruled surfaces that are normal or tangent to <em>M</em> and give some geometric relations between them, generalizing some recent results obtained in <span>[3]</span>, <span>[5]</span>. We also give some general properties on normal and tangent submanifolds of arbitrary dimension.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some geometric properties of normal and tangent submanifolds\",\"authors\":\"Josué Meléndez, Eduardo Rodríguez-Romero\",\"doi\":\"10.1016/j.difgeo.2023.102063\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we study some special ruled surfaces in a 3-dimensional Riemannian manifold <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>. Given an immersed surface <em>M</em> into <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>, we consider the ruled surfaces that are normal or tangent to <em>M</em> and give some geometric relations between them, generalizing some recent results obtained in <span>[3]</span>, <span>[5]</span>. We also give some general properties on normal and tangent submanifolds of arbitrary dimension.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S092622452300089X\",\"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":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S092622452300089X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some geometric properties of normal and tangent submanifolds
In this paper we study some special ruled surfaces in a 3-dimensional Riemannian manifold . Given an immersed surface M into , we consider the ruled surfaces that are normal or tangent to M and give some geometric relations between them, generalizing some recent results obtained in [3], [5]. We also give some general properties on normal and tangent submanifolds of arbitrary dimension.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.