Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916501961834496 |
|---|---|
| author | Beran, Tobias |
| author_facet | Beran, Tobias |
| contents | We prove a synthetic Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces with global curvature bounded below by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$: It states that the space necessarily is a warped product with warping function $\cos:(-\fracπ{2},\fracπ{2})\to\mathbb{R}_+$. From this, one also sees that a globally hyperbolic spacetime with curvature bounded above by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$ is a warped product with warping function $\cos$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces Beran, Tobias Differential Geometry Mathematical Physics Metric Geometry 53C50, 53C23, 53B30 We prove a synthetic Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces with global curvature bounded below by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$: It states that the space necessarily is a warped product with warping function $\cos:(-\fracπ{2},\fracπ{2})\to\mathbb{R}_+$. From this, one also sees that a globally hyperbolic spacetime with curvature bounded above by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$ is a warped product with warping function $\cos$. |
| title | Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces |
| topic | Differential Geometry Mathematical Physics Metric Geometry 53C50, 53C23, 53B30 |
| url | https://arxiv.org/abs/2401.17017 |