Torsion-free Connections with prescribed Curvature
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911900809297920 |
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| author | Basurto-Arzate, Efrain |
| author_facet | Basurto-Arzate, Efrain |
| contents | We provide necessary and sufficient conditions for a curvature map $S\colon U\longrightarrow K(\mathfrak{g})$ to arise from the curvature tensor of a torsion-free connection on a sufficiently small $U'\subset U$ by using a suitable power series approach. This torsion-free connection is uniquely given. The curvature map $S$ is used to effectively compute the holonomy of this connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torsion-free Connections with prescribed Curvature Basurto-Arzate, Efrain Differential Geometry 53B05, 53A55, 53C29 We provide necessary and sufficient conditions for a curvature map $S\colon U\longrightarrow K(\mathfrak{g})$ to arise from the curvature tensor of a torsion-free connection on a sufficiently small $U'\subset U$ by using a suitable power series approach. This torsion-free connection is uniquely given. The curvature map $S$ is used to effectively compute the holonomy of this connection. |
| title | Torsion-free Connections with prescribed Curvature |
| topic | Differential Geometry 53B05, 53A55, 53C29 |
| url | https://arxiv.org/abs/2406.01530 |