{"title":"关于凸性双流形的几何","authors":"Jacob Van Hook","doi":"10.1016/j.difgeo.2023.102081","DOIUrl":null,"url":null,"abstract":"<div><p><span><span><span>We consider complete locally irreducible conullity two Riemannian manifolds with constant </span>scalar curvature along </span>nullity geodesics. There exists a naturally defined open </span>dense subset on which we describe the metric in terms of several functions which are uniquely determined up to isometry. In addition, we show that the fundamental group is either trivial or infinite cyclic.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"92 ","pages":"Article 102081"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the geometry of conullity two manifolds\",\"authors\":\"Jacob Van Hook\",\"doi\":\"10.1016/j.difgeo.2023.102081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span><span>We consider complete locally irreducible conullity two Riemannian manifolds with constant </span>scalar curvature along </span>nullity geodesics. There exists a naturally defined open </span>dense subset on which we describe the metric in terms of several functions which are uniquely determined up to isometry. In addition, we show that the fundamental group is either trivial or infinite cyclic.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":\"92 \",\"pages\":\"Article 102081\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-11-23\",\"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/S0926224523001079\",\"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/S0926224523001079","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider complete locally irreducible conullity two Riemannian manifolds with constant scalar curvature along nullity geodesics. There exists a naturally defined open dense subset on which we describe the metric in terms of several functions which are uniquely determined up to isometry. In addition, we show that the fundamental group is either trivial or infinite cyclic.
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.
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