FOUR-DIMENSIONAL GRADIENT SHRINKING SOLITONS WITH PINCHED CURVATURE

被引：0

作者：

Zhang, Zhu-Hong ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 07期

关键词：

Ricci flow; maximum principle; pinched Weyl tensor; POSITIVE ISOTROPIC CURVATURE; RICCI SOLITONS; CLASSIFICATION; 4-MANIFOLDS; MANIFOLDS; FLOW;

D O I：

10.1090/proc/13859

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that any four-dimensional gradient shrinking soliton with pinched Weyl curvature (*) and satisfying c(1) <= R <= c(2) for some positive constant c(1) and c(2), will have nonnegative Ricci curvature. As a consequence, we prove that it must be a finite quotient of S-4, CP2, or S-3 x R. In particular, a compact four-dimensional gradient shrinking soliton with pinched Weyl curvature (*) must be S-4, RP4 or CP2.

引用

页码：3049 / 3056

页数：8

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