Uniqueness of the torsion-curvature pair
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909930857955328 |
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| author | Bohórquez, Raúl Martínez Navarro, José Sancho, Juan B. |
| author_facet | Bohórquez, Raúl Martínez Navarro, José Sancho, Juan B. |
| contents | On smooth manifolds of dimension $n \ge 4$, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that satisfy both the linear and differential Bianchi identities.
This result extends to arbitrary linear connections a recent characterisation of the curvature tensor of a symmetric linear connection obtained in the paper "On the uniqueness of the torsion and curvature operators", Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 114, 2020. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of the torsion-curvature pair Bohórquez, Raúl Martínez Navarro, José Sancho, Juan B. Differential Geometry On smooth manifolds of dimension $n \ge 4$, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that satisfy both the linear and differential Bianchi identities. This result extends to arbitrary linear connections a recent characterisation of the curvature tensor of a symmetric linear connection obtained in the paper "On the uniqueness of the torsion and curvature operators", Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 114, 2020. |
| title | Uniqueness of the torsion-curvature pair |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.22627 |