Time-dependent metrics and connections
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917211962081280 |
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| author | Gràcia, Xavier Rivas, Xavier Torres, Daniel |
| author_facet | Gràcia, Xavier Rivas, Xavier Torres, Daniel |
| contents | Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing the corresponding energy functional, but also through the introduction of a more general concept of time-dependent covariant derivative operator. This relies on the examination of connections on the product manifold $\mathbb{R}\times M$. For these time-dependent covariant derivatives we explore the notions of parallel transport, geodesics and torsion. We also define the derivative of a one-parameter family of connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time-dependent metrics and connections Gràcia, Xavier Rivas, Xavier Torres, Daniel Differential Geometry Mathematical Physics 53B15, 53B20, 53C05, 58E10 Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing the corresponding energy functional, but also through the introduction of a more general concept of time-dependent covariant derivative operator. This relies on the examination of connections on the product manifold $\mathbb{R}\times M$. For these time-dependent covariant derivatives we explore the notions of parallel transport, geodesics and torsion. We also define the derivative of a one-parameter family of connections. |
| title | Time-dependent metrics and connections |
| topic | Differential Geometry Mathematical Physics 53B15, 53B20, 53C05, 58E10 |
| url | https://arxiv.org/abs/2601.14064 |