{"title":"德西特空间 dSn-1,1 上同调为零或一的行为","authors":"H. Mahdiloo , P. Ahmadi , M. Hassani","doi":"10.1016/j.difgeo.2024.102180","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this paper is to classify the connected Lie groups which act isometrically and with cohomogeneity <em>c</em>, where <span><math><mi>c</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>, on the de Sitter space <span><math><mi>d</mi><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> up to conjugacy in <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and then up to orbit equivalence. Among other results, we give the list of the groups represented in the isometry group of the de Sitter space <span><math><mi>d</mi><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"97 ","pages":"Article 102180"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Actions with cohomogeneity zero or one on the de Sitter space dSn−1,1\",\"authors\":\"H. Mahdiloo , P. Ahmadi , M. Hassani\",\"doi\":\"10.1016/j.difgeo.2024.102180\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The aim of this paper is to classify the connected Lie groups which act isometrically and with cohomogeneity <em>c</em>, where <span><math><mi>c</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>, on the de Sitter space <span><math><mi>d</mi><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> up to conjugacy in <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and then up to orbit equivalence. Among other results, we give the list of the groups represented in the isometry group of the de Sitter space <span><math><mi>d</mi><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":\"97 \",\"pages\":\"Article 102180\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-03\",\"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/S0926224524000731\",\"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/S0926224524000731","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Actions with cohomogeneity zero or one on the de Sitter space dSn−1,1
The aim of this paper is to classify the connected Lie groups which act isometrically and with cohomogeneity c, where , on the de Sitter space up to conjugacy in and then up to orbit equivalence. Among other results, we give the list of the groups represented in the isometry group of the de Sitter space .
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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