Generalized almost-Kähler–Ricci solitons

IF 0.6 4区 数学 Q3 MATHEMATICS Differential Geometry and its Applications Pub Date : 2024-10-23 DOI:10.1016/j.difgeo.2024.102193
{"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}
引用次数: 0

Abstract

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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
广义的近凯勒-里奇孤子
我们将 Kähler-Ricci 孤子概括为近 Kähler 设定的井上矩图[25]的零点,并证明它们的存在阻碍了紧凑交映法诺流形上第一切恩-爱因斯坦近 Kähler 度量的存在。我们证明了 4 维情况下此类度量的变形结果。此外,我们还研究了 2n 维紧凑交折射法诺流形上全形向量场的李代数,它允许广义的近凯勒-里奇孤子。特别是,我们将松岛定理[41]部分扩展到了紧凑的第一切恩-爱因斯坦近凯勒流形。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
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.
期刊最新文献
Generalized almost-Kähler–Ricci solitons Deforming locally convex curves into curves of constant k-order width Covariant Schrödinger operator and L2-vanishing property on Riemannian manifolds Nearly half-flat SU(3) structures on S3 × S3 Vector bundle automorphisms preserving Morse-Bott foliations
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1