Classification of gradient steady Ricci solitons with linear curvature decay

被引:0
作者
Yuxing Deng
Xiaohua Zhu
机构
[1] Beijing Institute of Technology,School of Mathematics and Statistics
[2] Peking University,School of Mathematical Sciences and BICMR
来源
Science China Mathematics | 2020年 / 63卷
关键词
Ricci flow; steady Ricci solitons; rotational symmetry; 53C25; 53C55; 58J05;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we study steady Ricci solitons with a linear decay of sectional curvature. In particular, we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional κ-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.
引用
收藏
页码:135 / 154
页数:19
相关论文
共 20 条
[1]  
Brendle S(2013)Rotational symmetry of self-similar solutions to the Ricci flow Invent Math 194 731-764
[2]  
Brendle S(2014)Rotational symmetry of Ricci solitons in higher dimensions J Differential Geom 97 191-214
[3]  
Cao H D(2012)On locally conformally flat gradient steady Ricci solitons Trans Amer Math Soc 364 2377-2391
[4]  
Chen Q(2009)Strong uniqueness of the Ricci flow J Differential Geom 82 363-382
[5]  
Chen B L(2009)Some new examples of non-Kahler Ricci solitons Math Res Lett 16 349-363
[6]  
Dancer A(2019)Three-dimensional steady gradient Ricci solitons with linear curvature decay Int Math Res Not IMRN 4 1108-1124
[7]  
Wang M(1978)Almost flat manifolds J Differential Geom 13 231-241
[8]  
Deng Y X(2015)A rigidity theorem for codimension one shrinking gradient Ricci solitons in ℝ Calc Var Partial Differential Equations 54 4019-4036
[9]  
Zhu X H(1995)A compactness property for solutions of the Ricci flow Amer J Math 117 545-572
[10]  
Gromov M(2019)Poisson equation on complete manifolds Adv Math 348 81-145