常截面曲率可分离超曲面的分类

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI:10.1016/j.jmaa.2025.129859

Muhittin Evren Aydin , Rafael López , Gabriel-Eduard Vîlcu

{"title":"常截面曲率可分离超曲面的分类","authors":"Muhittin Evren Aydin , Rafael López , Gabriel-Eduard Vîlcu","doi":"10.1016/j.jmaa.2025.129859","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean <em>n</em>-space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In dimension <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, this classification was solved by Hasanis and López (2021) <span><span>[18]</span></span>. When <span><math><mi>n</mi><mo>></mo><mn>3</mn></math></span>, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129859"},"PeriodicalIF":1.2000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of separable hypersurfaces with constant sectional curvature\",\"authors\":\"Muhittin Evren Aydin , Rafael López , Gabriel-Eduard Vîlcu\",\"doi\":\"10.1016/j.jmaa.2025.129859\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean <em>n</em>-space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In dimension <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, this classification was solved by Hasanis and López (2021) <span><span>[18]</span></span>. When <span><math><mi>n</mi><mo>></mo><mn>3</mn></math></span>, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"553 1\",\"pages\":\"Article 129859\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X25006407\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25006407","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文给出了欧氏n空间Rn中常截面曲率可分离超曲面的完整分类。在维度n=3中，该分类由Hasanis和López(2021)[18]解决。当n>；3时，我们证明了零截面曲率的可分离超曲面是这类超曲面的三个特殊族。最后，我们证明了超球是唯一具有非零常截面曲率的可分离超曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Classification of separable hypersurfaces with constant sectional curvature

In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean n-space

R^{n}

. In dimension

n = 3

, this classification was solved by Hasanis and López (2021) [18]. When

n > 3

, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional 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

来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.