Weyl-type theorems in Galilei and Carroll geometry
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911735929110528 |
|---|---|
| author | Schwartz, Philip K. Read, James Vigneron, Quentin |
| author_facet | Schwartz, Philip K. Read, James Vigneron, Quentin |
| contents | A classic theorem of Weyl (1921) states that a Weyl metric -- a natural generalisation of a pseudo-Riemannian metric -- is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal structure is uniquely determined by its projective structure. We discuss analogous results for suitably defined notions of conformal structure for Galilei and Carroll geometry, i.e. for spacetime geometries arising as the `non-relativistic' and `ultra-relativistic' limits of Lorentzian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weyl-type theorems in Galilei and Carroll geometry Schwartz, Philip K. Read, James Vigneron, Quentin Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry History and Philosophy of Physics A classic theorem of Weyl (1921) states that a Weyl metric -- a natural generalisation of a pseudo-Riemannian metric -- is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal structure is uniquely determined by its projective structure. We discuss analogous results for suitably defined notions of conformal structure for Galilei and Carroll geometry, i.e. for spacetime geometries arising as the `non-relativistic' and `ultra-relativistic' limits of Lorentzian geometry. |
| title | Weyl-type theorems in Galilei and Carroll geometry |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry History and Philosophy of Physics |
| url | https://arxiv.org/abs/2606.00799 |