Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2504.14710 |
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Inhaltsangabe:
- 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.