Steady Ricci solitons with horizontally ε-pinched Ricci curvature

2016/01/09 by Deng, Yuxing, Zhu, Xiaohua
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.02111

Abstract

In this paper, we prove that any κ-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally ε-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any κ-noncollapsed gradient steady Ricci soliton (Mⁿ, g,f) with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature R(x) satisfies lim_r(x)→∞R(x)f(x)=C₀sup_{x∈ M}R(x) with C₀>(n-2)/(2).

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