{"title":"LCK溶剂流形上的Vaisman结构","authors":"Hiroshi Sawai","doi":"10.21099/tkbjm/20234701001","DOIUrl":null,"url":null,"abstract":"The purpose in this paper is to give necessary and sufficient conditions for an LCK structure to be a Vaisman structure on a solvmanifold with a left-invariant complex structure. As an application, we determine a Vaisman solvmanifold such that the commutator of the solvable Lie group is abelian.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"151 1","pages":"0"},"PeriodicalIF":0.3000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"VAISMAN STRUCTURES ON LCK SOLVMANIFOLDS\",\"authors\":\"Hiroshi Sawai\",\"doi\":\"10.21099/tkbjm/20234701001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose in this paper is to give necessary and sufficient conditions for an LCK structure to be a Vaisman structure on a solvmanifold with a left-invariant complex structure. As an application, we determine a Vaisman solvmanifold such that the commutator of the solvable Lie group is abelian.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":\"151 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/tkbjm/20234701001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/tkbjm/20234701001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The purpose in this paper is to give necessary and sufficient conditions for an LCK structure to be a Vaisman structure on a solvmanifold with a left-invariant complex structure. As an application, we determine a Vaisman solvmanifold such that the commutator of the solvable Lie group is abelian.
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