Rigidity of compact rank one symmetric spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909214752899072 |
|---|---|
| author | Connell, Chris Islam, Mitul Nguyen, Thang Spatzier, Ralf |
| author_facet | Connell, Chris Islam, Mitul Nguyen, Thang Spatzier, Ralf |
| contents | We consider rigidity properties of compact symmetric spaces $X$ with metric $g_0$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $κ$ bounded by $0 \leq κ\leq 1$. If $g$ equals $g_0$ outside a convex proper subset of $X$, then $g$ is isometric with $g_0$. We also exhibit examples of surfaces showing that the nonnegativity of the curvature is needed. Our main result complements earlier results on other symmetric spaces by Gromov and Schroeder-Ziller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of compact rank one symmetric spaces Connell, Chris Islam, Mitul Nguyen, Thang Spatzier, Ralf Differential Geometry 53C24 (Primary) 53C20, 53C35 (Secondary) We consider rigidity properties of compact symmetric spaces $X$ with metric $g_0$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $κ$ bounded by $0 \leq κ\leq 1$. If $g$ equals $g_0$ outside a convex proper subset of $X$, then $g$ is isometric with $g_0$. We also exhibit examples of surfaces showing that the nonnegativity of the curvature is needed. Our main result complements earlier results on other symmetric spaces by Gromov and Schroeder-Ziller. |
| title | Rigidity of compact rank one symmetric spaces |
| topic | Differential Geometry 53C24 (Primary) 53C20, 53C35 (Secondary) |
| url | https://arxiv.org/abs/2406.00558 |