{"title":"广义的近凯勒-里奇孤子","authors":"","doi":"10.1016/j.difgeo.2024.102193","DOIUrl":null,"url":null,"abstract":"<div><div>We generalize Kähler–Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map <span><span>[25]</span></span>, and show that their existence is an obstruction to the existence of first-Chern–Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the 4-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on 2<em>n</em>-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler–Ricci solitons. In particular, we partially extend Matsushima's theorem <span><span>[41]</span></span> to compact first-Chern–Einstein almost-Kähler manifolds.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized almost-Kähler–Ricci solitons\",\"authors\":\"\",\"doi\":\"10.1016/j.difgeo.2024.102193\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We generalize Kähler–Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map <span><span>[25]</span></span>, and show that their existence is an obstruction to the existence of first-Chern–Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the 4-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on 2<em>n</em>-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler–Ricci solitons. In particular, we partially extend Matsushima's theorem <span><span>[41]</span></span> to compact first-Chern–Einstein almost-Kähler manifolds.</div></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S092622452400086X\",\"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":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S092622452400086X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We generalize Kähler–Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map [25], and show that their existence is an obstruction to the existence of first-Chern–Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the 4-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on 2n-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler–Ricci solitons. In particular, we partially extend Matsushima's theorem [41] to compact first-Chern–Einstein almost-Kähler manifolds.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.