{"title":"Einstein幂自由基上的伪代数Ricci孤子","authors":"Zaili Yan","doi":"10.1515/advgeom-2020-0032","DOIUrl":null,"url":null,"abstract":"Abstract We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups.As applications, we prove that every Einstein nilradical admits a non-Riemannian algebraic Ricci soliton, and that any algebraic Ricci soliton on a semi-simple Lie group is Einstein. Furthermore, we construct several Lorentz algebraic Ricci solitons on the nilpotent Lie groups which have a codimension one abelian ideal.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/advgeom-2020-0032","citationCount":"2","resultStr":"{\"title\":\"Pseudo-algebraic Ricci solitons on Einstein nilradicals\",\"authors\":\"Zaili Yan\",\"doi\":\"10.1515/advgeom-2020-0032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups.As applications, we prove that every Einstein nilradical admits a non-Riemannian algebraic Ricci soliton, and that any algebraic Ricci soliton on a semi-simple Lie group is Einstein. Furthermore, we construct several Lorentz algebraic Ricci solitons on the nilpotent Lie groups which have a codimension one abelian ideal.\",\"PeriodicalId\":7335,\"journal\":{\"name\":\"Advances in Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/advgeom-2020-0032\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/advgeom-2020-0032\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2020-0032","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Pseudo-algebraic Ricci solitons on Einstein nilradicals
Abstract We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups.As applications, we prove that every Einstein nilradical admits a non-Riemannian algebraic Ricci soliton, and that any algebraic Ricci soliton on a semi-simple Lie group is Einstein. Furthermore, we construct several Lorentz algebraic Ricci solitons on the nilpotent Lie groups which have a codimension one abelian ideal.
期刊介绍：
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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