{"title":"一般不定度量的贝特曼变换的推广","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.45.7","DOIUrl":null,"url":null,"abstract":"Bateman’s transformation is associated with the Lorentzian metric and preserves solutions of the wave equation. We generalize Bateman’s transformation for general indefinite semi-euclidean metrics. Then we show that the generalized transformation preserves solutions of the equation associated with given indefinite metric.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"22 1","pages":"7-13"},"PeriodicalIF":0.0000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Generalizations of Bateman's transformation for general indefinite metrics\",\"authors\":\"Katsunori Shimomura\",\"doi\":\"10.5036/MJIU.45.7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bateman’s transformation is associated with the Lorentzian metric and preserves solutions of the wave equation. We generalize Bateman’s transformation for general indefinite semi-euclidean metrics. Then we show that the generalized transformation preserves solutions of the equation associated with given indefinite metric.\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"22 1\",\"pages\":\"7-13\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/MJIU.45.7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.45.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalizations of Bateman's transformation for general indefinite metrics
Bateman’s transformation is associated with the Lorentzian metric and preserves solutions of the wave equation. We generalize Bateman’s transformation for general indefinite semi-euclidean metrics. Then we show that the generalized transformation preserves solutions of the equation associated with given indefinite metric.
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