{"title":"伪黎曼对称 R 空间的对偶集","authors":"Kyoji Sugimoto","doi":"10.1016/j.difgeo.2023.102104","DOIUrl":null,"url":null,"abstract":"<div><p>We show that antipodal sets of pseudo-Riemannian symmetric <em>R</em>-spaces associated with non-degenerate Jordan triple systems satisfy the following two properties: (1) Any antipodal set is included in a great antipodal set, and (2) any two great antipodal sets are transformed into each other by an isometry.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Antipodal sets of pseudo-Riemannian symmetric R-spaces\",\"authors\":\"Kyoji Sugimoto\",\"doi\":\"10.1016/j.difgeo.2023.102104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We show that antipodal sets of pseudo-Riemannian symmetric <em>R</em>-spaces associated with non-degenerate Jordan triple systems satisfy the following two properties: (1) Any antipodal set is included in a great antipodal set, and (2) any two great antipodal sets are transformed into each other by an isometry.</p></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-01-08\",\"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/S0926224523001304\",\"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/S0926224523001304","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
我们证明，与非退化约旦三重系统相关联的伪黎曼对称 R 空间的反交点集合满足以下两个性质：（1）任何反交点集合都包含在一个大反交点集合中；（2）任何两个大反交点集合都通过等距法相互转化。
Antipodal sets of pseudo-Riemannian symmetric R-spaces
We show that antipodal sets of pseudo-Riemannian symmetric R-spaces associated with non-degenerate Jordan triple systems satisfy the following two properties: (1) Any antipodal set is included in a great antipodal set, and (2) any two great antipodal sets are transformed into each other by an isometry.
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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