Four-dimensional complete gradient shrinking Ricci solitons
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910362374242304 |
|---|---|
| author | Cao, Huai-Dong Ribeiro Jr, Ernani Zhou, Detang |
| author_facet | Cao, Huai-Dong Ribeiro Jr, Ernani Zhou, Detang |
| contents | In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton $\Bbb{R}^4,$ or $\Bbb{S}^{3}\times\Bbb{R}$, or $\Bbb{S}^{2}\times\Bbb{R}^{2}.$ In addition, we provide some curvature estimates for four-dimensional complete gradient Ricci solitons assuming that its scalar curvature is suitable bounded by the potential function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_13066 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Four-dimensional complete gradient shrinking Ricci solitons Cao, Huai-Dong Ribeiro Jr, Ernani Zhou, Detang Differential Geometry In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton $\Bbb{R}^4,$ or $\Bbb{S}^{3}\times\Bbb{R}$, or $\Bbb{S}^{2}\times\Bbb{R}^{2}.$ In addition, we provide some curvature estimates for four-dimensional complete gradient Ricci solitons assuming that its scalar curvature is suitable bounded by the potential function. |
| title | Four-dimensional complete gradient shrinking Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2006.13066 |