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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2504.14710 |
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| _version_ | 1866916699023867904 |
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| author | Sánchez, Miguel Villaseñor, Fidel F. |
| author_facet | Sánchez, Miguel Villaseñor, Fidel F. |
| contents | The space of anisotropic $r$-contravariant $s$-covariant $α$-homogeneous tensors on a manifold admits a functorial structure where vertical derivatives $\dot{\partial}$ and contractions $\imath_{\mathbb{C}}$ by the Liouville vector field $\mathbb{C}$ are operators which maintain $s+α$ constant. In (semi-)Finsler geometry, this structure is transmitted faithfully to connection-type elements yielding the following ladder: geodesic sprays / nonlinear connections / anisotropic connections / linear (Finslerian) connections. However, it is more loosely transmitted to metric-type ones: Finslerian Lagrangians / Legendre transformations / anisotropic metrics. We will study this structure in depth and apply it to discuss the recent variational proposals (Einstein-Hilbert, Einstein-Palatini, Einstein-Cartan) for generalizing Einstein equations to the Finsler setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The ladder of Finsler-type objects and their variational problems on spacetimes Sánchez, Miguel Villaseñor, Fidel F. Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53B40 (Primary) 49S05 (Secondary) The space of anisotropic $r$-contravariant $s$-covariant $α$-homogeneous tensors on a manifold admits a functorial structure where vertical derivatives $\dot{\partial}$ and contractions $\imath_{\mathbb{C}}$ by the Liouville vector field $\mathbb{C}$ are operators which maintain $s+α$ constant. In (semi-)Finsler geometry, this structure is transmitted faithfully to connection-type elements yielding the following ladder: geodesic sprays / nonlinear connections / anisotropic connections / linear (Finslerian) connections. However, it is more loosely transmitted to metric-type ones: Finslerian Lagrangians / Legendre transformations / anisotropic metrics. We will study this structure in depth and apply it to discuss the recent variational proposals (Einstein-Hilbert, Einstein-Palatini, Einstein-Cartan) for generalizing Einstein equations to the Finsler setting. |
| title | The ladder of Finsler-type objects and their variational problems on spacetimes |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53B40 (Primary) 49S05 (Secondary) |
| url | https://arxiv.org/abs/2504.14710 |