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arXiv · 2101.12681

Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature

Fengjiang Li
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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 ($n\geq 5$) 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 $n\ge 5$, 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.

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Fengjiang Li. 2021-01-29. Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature. https://arxiv.org/abs/2101.12681

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