The curvature operator of the second kind in dimension three
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917595820589056 |
|---|---|
| author | Fluck, Harry Li, Xiaolong |
| author_facet | Fluck, Harry Li, Xiaolong |
| contents | This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that $\a$-positive/$\a$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all $\a \in [1,5]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The curvature operator of the second kind in dimension three Fluck, Harry Li, Xiaolong Differential Geometry 53E20, 53C21 This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that $\a$-positive/$\a$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all $\a \in [1,5]$. |
| title | The curvature operator of the second kind in dimension three |
| topic | Differential Geometry 53E20, 53C21 |
| url | https://arxiv.org/abs/2303.17663 |