{"title":"关于非紧化梯度孤子","authors":"Antonio W. Cunha, Erin Griffin","doi":"10.1007/s10455-023-09904-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we extend existing results for generalized solitons, called <i>q</i>-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field <i>X</i> and curvature conditions on <i>M</i>, we are able to use the chosen properties of the tensor <i>q</i> to see that such non-compact <i>q</i>-solitons are stationary and <i>q</i>-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On non-compact gradient solitons\",\"authors\":\"Antonio W. Cunha, Erin Griffin\",\"doi\":\"10.1007/s10455-023-09904-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we extend existing results for generalized solitons, called <i>q</i>-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field <i>X</i> and curvature conditions on <i>M</i>, we are able to use the chosen properties of the tensor <i>q</i> to see that such non-compact <i>q</i>-solitons are stationary and <i>q</i>-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10455-023-09904-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-023-09904-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we extend existing results for generalized solitons, called q-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field X and curvature conditions on M, we are able to use the chosen properties of the tensor q to see that such non-compact q-solitons are stationary and q-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.