On the classification of four-dimensional gradient Ricci solitons

被引:2
作者
Yang, Fei [1 ]
Zhang, Liangdi [2 ,3 ]
机构
[1] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China
[2] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China
[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
关键词
Classification; Four dimension; Gradient Ricci solitons; Divergence -free curvature; ROTATIONAL SYMMETRY; RIGIDITY;
D O I
10.1016/j.difgeo.2022.101936
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we prove some classification results for four-dimensional gradient Ricci solitons. For a four-dimensional gradient shrinking Ricci soliton with div4Rm +/- = 0, we show that it is either Einstein or a finite quotient of R4, S2 x R2 or S3 x R. The same result can be obtained under the condition of div4W +/- = 0. We also present some classification results of four-dimensional complete non-compact gradient expanding Ricci soliton with non-negative Ricci curvature and gradient steady Ricci solitons under certain curvature conditions. (c) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数:23
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