具有下有界标量曲率$\mathbb{H}^n/\mathbb{Z}^{n-2}$的刚性和非刚性

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-01 DOI:10.3842/sigma.2023.083

Tianze Hao, Yuhao Hu, Peng Liu, Yuguang Shi

{"title":"具有下有界标量曲率$\\mathbb{H}^n/\\mathbb{Z}^{n-2}$的刚性和非刚性","authors":"Tianze Hao, Yuhao Hu, Peng Liu, Yuguang Shi","doi":"10.3842/sigma.2023.083","DOIUrl":null,"url":null,"abstract":"We show that the hyperbolic manifold $\\mathbb{H}^n/\\mathbb{Z}^{n-2}$ is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound $-n(n-1)$, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":"56 1","pages":"0"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rigidity and Non-Rigidity of $\\\\mathbb{H}^n/\\\\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below\",\"authors\":\"Tianze Hao, Yuhao Hu, Peng Liu, Yuguang Shi\",\"doi\":\"10.3842/sigma.2023.083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the hyperbolic manifold $\\\\mathbb{H}^n/\\\\mathbb{Z}^{n-2}$ is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound $-n(n-1)$, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.\",\"PeriodicalId\":49453,\"journal\":{\"name\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3842/sigma.2023.083\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3842/sigma.2023.083","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了双曲流形$\mathbb{H}^n/\mathbb{Z}^{n-2}$在所有保持标量曲率下界$-n(n-1)$的紧支撑变形下不是刚性的，并且在进一步受某些拓扑条件约束的变形下是刚性的。此外，我们还证明了两个相关的分裂结果。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Rigidity and Non-Rigidity of $\mathbb{H}^n/\mathbb{Z}^{n-2}$ with Scalar Curvature Bounded from Below

We show that the hyperbolic manifold $\mathbb{H}^n/\mathbb{Z}^{n-2}$ is not rigid under all compactly supported deformations that preserve the scalar curvature lower bound $-n(n-1)$, and that it is rigid under deformations that are further constrained by certain topological conditions. In addition, we prove two related splitting results.

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

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.