{"title":"紧凑型准 Sasaki-Ricci Solitons 的间隙定理","authors":"Xiaosheng Li, Fanqi Zeng","doi":"10.1007/s44198-024-00227-8","DOIUrl":null,"url":null,"abstract":"<p>Gradient quasi Sasaki–Ricci solitons are generalization of gradient Sasaki–Ricci solitons and Sasaki–Einstein manifolds. The main focus of this paper is to establish two gap results for the transverse Ricci curvature <span>\\({\\rm Ric}^{T}\\)</span> and the transverse scalar curvature <span>\\({\\mathscr {S}}^{T}\\)</span>, based on which we can derive necessary and sufficient conditions for gradient quasi Sasaki–Ricci solitons to be Sasaki–Einstein. Our results generalize some recent works on this direction.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"275 3 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gap Theorems for Compact Quasi Sasaki–Ricci Solitons\",\"authors\":\"Xiaosheng Li, Fanqi Zeng\",\"doi\":\"10.1007/s44198-024-00227-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Gradient quasi Sasaki–Ricci solitons are generalization of gradient Sasaki–Ricci solitons and Sasaki–Einstein manifolds. The main focus of this paper is to establish two gap results for the transverse Ricci curvature <span>\\\\({\\\\rm Ric}^{T}\\\\)</span> and the transverse scalar curvature <span>\\\\({\\\\mathscr {S}}^{T}\\\\)</span>, based on which we can derive necessary and sufficient conditions for gradient quasi Sasaki–Ricci solitons to be Sasaki–Einstein. Our results generalize some recent works on this direction.</p>\",\"PeriodicalId\":48904,\"journal\":{\"name\":\"Journal of Nonlinear Mathematical Physics\",\"volume\":\"275 3 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s44198-024-00227-8\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00227-8","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Gap Theorems for Compact Quasi Sasaki–Ricci Solitons
Gradient quasi Sasaki–Ricci solitons are generalization of gradient Sasaki–Ricci solitons and Sasaki–Einstein manifolds. The main focus of this paper is to establish two gap results for the transverse Ricci curvature \({\rm Ric}^{T}\) and the transverse scalar curvature \({\mathscr {S}}^{T}\), based on which we can derive necessary and sufficient conditions for gradient quasi Sasaki–Ricci solitons to be Sasaki–Einstein. Our results generalize some recent works on this direction.
期刊介绍:
Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles.
Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics.
The main subjects are:
-Nonlinear Equations of Mathematical Physics-
Quantum Algebras and Integrability-
Discrete Integrable Systems and Discrete Geometry-
Applications of Lie Group Theory and Lie Algebras-
Non-Commutative Geometry-
Super Geometry and Super Integrable System-
Integrability and Nonintegrability, Painleve Analysis-
Inverse Scattering Method-
Geometry of Soliton Equations and Applications of Twistor Theory-
Classical and Quantum Many Body Problems-
Deformation and Geometric Quantization-
Instanton, Monopoles and Gauge Theory-
Differential Geometry and Mathematical Physics