通过局部范围的标量曲率

Pub Date : 2017-10-05 DOI:10.1515/agms-2018-0008

G. Veronelli

{"title":"通过局部范围的标量曲率","authors":"G. Veronelli","doi":"10.1515/agms-2018-0008","DOIUrl":null,"url":null,"abstract":"Abstract We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2018-0008","citationCount":"4","resultStr":"{\"title\":\"Scalar Curvature via Local Extent\",\"authors\":\"G. Veronelli\",\"doi\":\"10.1515/agms-2018-0008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2017-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/agms-2018-0008\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/agms-2018-0008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2018-0008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

摘要

摘要给出了光滑黎曼流形标量曲率的度量表征，分析了点的无限小邻域中(n + 1)个点之间的最大距离。由于这种表征纯粹是用距离函数表示的，它可以用来解决在非光滑度量空间上定义标量曲率的问题。在第二部分中，我们将讨论这个问题，特别关注具有有界积分曲率的Alexandrov空间和曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Scalar Curvature via Local Extent

Abstract We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助