On the stability of the quaternion projective space
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911103498321920 |
|---|---|
| author | Neacşu, Crina-Daniela |
| author_facet | Neacşu, Crina-Daniela |
| contents | The aim of this note is to prove that the index of the identity map on a quaternion space form of constant quaternion sectional curvature $c$ is zero, provided that $c<0$. As an immediate consequence, it is established that any compact quaternion space form of negative quaternion sectional curvature is stable and it is emphasized that, on the contrary (but in agreement with some known results), any quaternion projective space is unstable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the stability of the quaternion projective space Neacşu, Crina-Daniela Differential Geometry 58E20 The aim of this note is to prove that the index of the identity map on a quaternion space form of constant quaternion sectional curvature $c$ is zero, provided that $c<0$. As an immediate consequence, it is established that any compact quaternion space form of negative quaternion sectional curvature is stable and it is emphasized that, on the contrary (but in agreement with some known results), any quaternion projective space is unstable. |
| title | On the stability of the quaternion projective space |
| topic | Differential Geometry 58E20 |
| url | https://arxiv.org/abs/2508.09315 |