Lie theory of the slice Riemannian geometry on the quaternionic unit ball
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_ | 1866910845410213888 |
|---|---|
| author | Quiroga-Barranco, Raul |
| author_facet | Quiroga-Barranco, Raul |
| contents | The quaternionic unit ball carries a Riemannian metric built using regular Möbius transformations: the slice Riemannian metric. We prove that the geometry induced by this metric is strongly related to the group $\mathrm{Sp}(1,1)$. We also develop the foundations for a Lie theoretic study of the slice Riemannian metric. In particular, we compute its isometry group and prove that it is built from symmetries of the Lie group $\mathrm{Sp}(1,1)$. We also compare the slice Riemannian geometry with the quaternionic Poincaré geometry, where the latter is considered within the setup of Riemannian symmetric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie theory of the slice Riemannian geometry on the quaternionic unit ball Quiroga-Barranco, Raul Differential Geometry Complex Variables Primary 30G35, Secondary 22F50 The quaternionic unit ball carries a Riemannian metric built using regular Möbius transformations: the slice Riemannian metric. We prove that the geometry induced by this metric is strongly related to the group $\mathrm{Sp}(1,1)$. We also develop the foundations for a Lie theoretic study of the slice Riemannian metric. In particular, we compute its isometry group and prove that it is built from symmetries of the Lie group $\mathrm{Sp}(1,1)$. We also compare the slice Riemannian geometry with the quaternionic Poincaré geometry, where the latter is considered within the setup of Riemannian symmetric spaces. |
| title | Lie theory of the slice Riemannian geometry on the quaternionic unit ball |
| topic | Differential Geometry Complex Variables Primary 30G35, Secondary 22F50 |
| url | https://arxiv.org/abs/2502.18669 |