{"title":"关于几乎* -里奇孤子","authors":"S. Kundu, S. Halder, K. De","doi":"10.56947/gjom.v13i2.790","DOIUrl":null,"url":null,"abstract":"Abstract. In the present paper, we prove three fundamental results concerning almost ∗-Ricci soliton in the framework of para-Sasakian manifold. The paper is organised as follows:• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is Jacobi along Reeb vector field ξ, then g becomes a ∗-Ricci soliton.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V as infinitesimal paracontact transformation, then V is killing and g is η-Einstein.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is collinear with the Reeb vector field ξ, then λ = 0, V is strict and g is η-Einstein.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On almost ∗-Ricci soliton\",\"authors\":\"S. Kundu, S. Halder, K. De\",\"doi\":\"10.56947/gjom.v13i2.790\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. In the present paper, we prove three fundamental results concerning almost ∗-Ricci soliton in the framework of para-Sasakian manifold. The paper is organised as follows:• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is Jacobi along Reeb vector field ξ, then g becomes a ∗-Ricci soliton.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V as infinitesimal paracontact transformation, then V is killing and g is η-Einstein.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is collinear with the Reeb vector field ξ, then λ = 0, V is strict and g is η-Einstein.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gulf Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56947/gjom.v13i2.790\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v13i2.790","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract. In the present paper, we prove three fundamental results concerning almost ∗-Ricci soliton in the framework of para-Sasakian manifold. The paper is organised as follows:• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is Jacobi along Reeb vector field ξ, then g becomes a ∗-Ricci soliton.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V as infinitesimal paracontact transformation, then V is killing and g is η-Einstein.• If a para-Sasakian metric g represents an almost ∗-Ricci soliton with potential vector field V is collinear with the Reeb vector field ξ, then λ = 0, V is strict and g is η-Einstein.