{"title":"LCK空间的Vaisman定理","authors":"Ovidiu Preda, Miron Stanciu","doi":"10.2422/2036-2145.202201_006","DOIUrl":null,"url":null,"abstract":". Vaisman’s theorem for locally conformally K¨ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K¨ahler metric is, in fact, globally conformally K¨ahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities. PN-III-P1-1.1-TE-2019-0262, within PNCDI III. Miron Stanciu was partially supported by a grant of Ministry of Research and Inno-vation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"228 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Vaisman theorem for LCK spaces\",\"authors\":\"Ovidiu Preda, Miron Stanciu\",\"doi\":\"10.2422/2036-2145.202201_006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Vaisman’s theorem for locally conformally K¨ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K¨ahler metric is, in fact, globally conformally K¨ahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities. PN-III-P1-1.1-TE-2019-0262, within PNCDI III. Miron Stanciu was partially supported by a grant of Ministry of Research and Inno-vation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.\",\"PeriodicalId\":8132,\"journal\":{\"name\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"volume\":\"228 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.202201_006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2422/2036-2145.202201_006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Vaisman’s theorem for locally conformally K¨ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K¨ahler metric is, in fact, globally conformally K¨ahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities. PN-III-P1-1.1-TE-2019-0262, within PNCDI III. Miron Stanciu was partially supported by a grant of Ministry of Research and Inno-vation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.
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