Metrizability of SO(3)-invariant connections: Riemann versus Finsler
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916349043802112 |
|---|---|
| author | Voicu, Nicoleta Elgendi, Salah Gomaa |
| author_facet | Voicu, Nicoleta Elgendi, Salah Gomaa |
| contents | For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi-Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald-Finsler) metrizability. In the present paper, we clarify, for 4-dimensional SO(3)-invariant, Berwald-Finsler metrizable connections, the issue of the existence of an affinely equivalent pseudo-Riemannian structure. In particular, we find all classes of SO(3)-invariant connections which are not Levi-Civita connections for any pseudo-Riemannian metric - hence, are non-metric in a conventional way - but can still be metrized by SO(3)-invariant Finsler functions. The implications for physics, together with some examples are briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metrizability of SO(3)-invariant connections: Riemann versus Finsler Voicu, Nicoleta Elgendi, Salah Gomaa Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53B40, 83D05 For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi-Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald-Finsler) metrizability. In the present paper, we clarify, for 4-dimensional SO(3)-invariant, Berwald-Finsler metrizable connections, the issue of the existence of an affinely equivalent pseudo-Riemannian structure. In particular, we find all classes of SO(3)-invariant connections which are not Levi-Civita connections for any pseudo-Riemannian metric - hence, are non-metric in a conventional way - but can still be metrized by SO(3)-invariant Finsler functions. The implications for physics, together with some examples are briefly discussed. |
| title | Metrizability of SO(3)-invariant connections: Riemann versus Finsler |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53B40, 83D05 |
| url | https://arxiv.org/abs/2404.02980 |