中心对称凸体的视锥特征

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-08-03 DOI:10.1515/advgeom-2022-0006

E. Morales-Amaya, J. Jer'onimo-Castro, D. J. Verdusco Hernández

{"title":"中心对称凸体的视锥特征","authors":"E. Morales-Amaya, J. Jer'onimo-Castro, D. J. Verdusco Hernández","doi":"10.1515/advgeom-2022-0006","DOIUrl":null,"url":null,"abstract":"Abstract We prove the following result: Let K be a strictly convex body in the Euclidean space ℝn, n ≥ 3, and let L be a hypersurface which is the image of an embedding of the sphere 𝕊n–1, such that K is contained in the interior of L. Suppose that, for every x ∈ L, there exists y ∈ L such that the support cones of K with apexes at x and y differ by a central symmetry. Then K and L are centrally symmetric and concentric.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A characterization of centrally symmetric convex bodies in terms of visual cones\",\"authors\":\"E. Morales-Amaya, J. Jer'onimo-Castro, D. J. Verdusco Hernández\",\"doi\":\"10.1515/advgeom-2022-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove the following result: Let K be a strictly convex body in the Euclidean space ℝn, n ≥ 3, and let L be a hypersurface which is the image of an embedding of the sphere 𝕊n–1, such that K is contained in the interior of L. Suppose that, for every x ∈ L, there exists y ∈ L such that the support cones of K with apexes at x and y differ by a central symmetry. Then K and L are centrally symmetric and concentric.\",\"PeriodicalId\":7335,\"journal\":{\"name\":\"Advances in Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/advgeom-2022-0006\",\"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":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2022-0006","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们证明了以下结果:设K是欧几里德空间(n, n≥3)上的一个严格凸体，设L是球面𝕊n-1的嵌入像的一个超曲面，使得K包含在L的内部。设对于每一个x∈L，存在y∈L使得K的顶锥在x和y有一个中心对称。那么K和L是中心对称和同心的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A characterization of centrally symmetric convex bodies in terms of visual cones

Abstract We prove the following result: Let K be a strictly convex body in the Euclidean space ℝn, n ≥ 3, and let L be a hypersurface which is the image of an embedding of the sphere 𝕊n–1, such that K is contained in the interior of L. Suppose that, for every x ∈ L, there exists y ∈ L such that the support cones of K with apexes at x and y differ by a central symmetry. Then K and L are centrally symmetric and concentric.

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

来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.