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arXiv · 2310.12529

$4d$ steady gradient Ricci solitons with nonnegative curvature away from a compact set

Ziyi Zhao·Xiaohua Zhu
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Abstract

In the paper, we analysis the asymptotic behavior of noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M, g)$ with nonnegative curvature operator away from a compact set $K$ of $M$. In particular, we prove: any $4d$ noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M^4, g)$ with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling if it admits a sequence of rescaled flows of $(M^4, g)$, which converges subsequently to a family of shrinking quotient cylinders.

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Ziyi Zhao, Xiaohua Zhu. 2023-10-19. $4d$ steady gradient Ricci solitons with nonnegative curvature away from a compact set. https://arxiv.org/abs/2310.12529

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