Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature

2021/01/29 by Li, Fengjiang · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.12681

Abstract

Our main aim in this paper is to investigate the rigidity of complete noncompact gradient steady Ricci solitons with harmonic Weyl tensor. More precisely, we prove that an n-dimensional (n≥ 5) complete noncompact gradient steady Ricci soliton with harmonic Weyl tensor and multiply warped product metric is either Ricci flat or isometric to the Bryant soliton up to scaling. Meanwhile, for n≥ 5, we provide a local structure theorem for n-dimensional connected (not necessarily complete) gradient Ricci solitons with harmonic Weyl curvature and multiply warped product metric.

Cited by

• The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
• Local Structure of Gradient Almost Ricci Solitons with Harmonic Weyl Tensor

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