{"title":"半阿波罗度规的等距","authors":"Peter Hästö *, Henri Lindén","doi":"10.1080/02781070410001712702","DOIUrl":null,"url":null,"abstract":"The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"37 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":"{\"title\":\"Isometries of the Half-Apollonian Metric\",\"authors\":\"Peter Hästö *, Henri Lindén\",\"doi\":\"10.1080/02781070410001712702\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.\",\"PeriodicalId\":272508,\"journal\":{\"name\":\"Complex Variables, Theory and Application: An International Journal\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Variables, Theory and Application: An International Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/02781070410001712702\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables, Theory and Application: An International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02781070410001712702","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The half-Apollonian metric is a generalization of the hyperbolic metric, similar to the Apollonian metric. It can be defined in arbitrary domains in the euclidean space and has the advantages of being easy to calculate and estimate. We show that the half-Apollonian metric has many geodesics and use this fact to show that in most domains all the isometries of the metric are similarity mappings.
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