Rigidity of positively curved Steady gradient Ricci solitons on orbifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912337734139904 |
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| author | Deng, Yuxing |
| author_facet | Deng, Yuxing |
| contents | In this paper, we study gradient Ricci soitons on smooth orbifolds. We prove that the scalar curvature of a complete shrinking or steady gradient Ricci soliton on an orbifold is nonnegative. We also show that a complete $κ$-noncollapsed steady gradient Ricci soliton on a Riemannian orbifold with positive curvature operator, compact singularity and linear curvature decay must be a finite quotient of the Bryant soliton. Finally, we show that a complete steady gradient Ricci soliton on a Riemannian orbifold with positive sectional curvature must be a finite quotient of the Bryant soliton if it is asymptotically quotient cylindrical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of positively curved Steady gradient Ricci solitons on orbifolds Deng, Yuxing Differential Geometry 53E20, 57R18, 58J05 In this paper, we study gradient Ricci soitons on smooth orbifolds. We prove that the scalar curvature of a complete shrinking or steady gradient Ricci soliton on an orbifold is nonnegative. We also show that a complete $κ$-noncollapsed steady gradient Ricci soliton on a Riemannian orbifold with positive curvature operator, compact singularity and linear curvature decay must be a finite quotient of the Bryant soliton. Finally, we show that a complete steady gradient Ricci soliton on a Riemannian orbifold with positive sectional curvature must be a finite quotient of the Bryant soliton if it is asymptotically quotient cylindrical. |
| title | Rigidity of positively curved Steady gradient Ricci solitons on orbifolds |
| topic | Differential Geometry 53E20, 57R18, 58J05 |
| url | https://arxiv.org/abs/2504.14525 |