$4d$ steady gradient Ricci solitons with nonnegative curvature away from a compact set
| Autor: | Zhao, Ziyi, Zhu, Xiaohua |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Proposition 4.1, Lemma 4.2 and Lemma 4.3 have been generalized for any dimension |
| Databáze: | arXiv |
| Externí odkaz: |
|