{"title":"具有关联仿射杀伤向量场的广义m-拟爱因斯坦流形的刚性结果。","authors":"Rahul Poddar, B. Subramanian, R. Sharma","doi":"10.36890/iejg.1286128","DOIUrl":null,"url":null,"abstract":"We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.\",\"authors\":\"Rahul Poddar, B. Subramanian, R. Sharma\",\"doi\":\"10.36890/iejg.1286128\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.\",\"PeriodicalId\":43768,\"journal\":{\"name\":\"International Electronic Journal of Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36890/iejg.1286128\",\"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":"International Electronic Journal of Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36890/iejg.1286128","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Rigidity Results On Generalized m-Quasi Einstein Manifolds with Associated Affine Killing Vector Field.
We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show that the same result holds for a complete non-trivial $m$-quasi Einstein manifold $M$ with finite $m$ and associated affine Killing vector field.
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