{"title":"局部可分解空间上某些连接的类曲率不变量的注记","authors":"N. Pušić","doi":"10.2298/pim1308219p","DOIUrl":null,"url":null,"abstract":"We consider an n-dimensional locally product space with p and q dimensional \n components (p + q = n) with parallel structure tensor, which means that such \n a space is locally decomposable. If we introduce a conformal transformation \n on such a space AB, it will have an invariant curvature-type tensor, the \n so-called product conformal curvature tensor (PC-tensor). Here we consider \n two connections, (F, g)-holomorphically semisymmetric one and \n F-holomorphically semisymmetric one, both with gradient generators. They \n both have curvature-like invariants and they are both equal to PC-tensor.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"20 7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A note on curvature-like invariants of some connections on locally decomposable spaces\",\"authors\":\"N. Pušić\",\"doi\":\"10.2298/pim1308219p\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider an n-dimensional locally product space with p and q dimensional \\n components (p + q = n) with parallel structure tensor, which means that such \\n a space is locally decomposable. If we introduce a conformal transformation \\n on such a space AB, it will have an invariant curvature-type tensor, the \\n so-called product conformal curvature tensor (PC-tensor). Here we consider \\n two connections, (F, g)-holomorphically semisymmetric one and \\n F-holomorphically semisymmetric one, both with gradient generators. They \\n both have curvature-like invariants and they are both equal to PC-tensor.\",\"PeriodicalId\":416273,\"journal\":{\"name\":\"Publications De L'institut Mathematique\",\"volume\":\"20 7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publications De L'institut Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/pim1308219p\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/pim1308219p","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on curvature-like invariants of some connections on locally decomposable spaces
We consider an n-dimensional locally product space with p and q dimensional
components (p + q = n) with parallel structure tensor, which means that such
a space is locally decomposable. If we introduce a conformal transformation
on such a space AB, it will have an invariant curvature-type tensor, the
so-called product conformal curvature tensor (PC-tensor). Here we consider
two connections, (F, g)-holomorphically semisymmetric one and
F-holomorphically semisymmetric one, both with gradient generators. They
both have curvature-like invariants and they are both equal to PC-tensor.