Variationality of conformal geodesics in dimension 3
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910101377384448 |
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| author | Kruglikov, Boris Matveev, Vladimir S. Steneker, Wijnand |
| author_facet | Kruglikov, Boris Matveev, Vladimir S. Steneker, Wijnand |
| contents | Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler--Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variationality of conformal geodesics in dimension 3 Kruglikov, Boris Matveev, Vladimir S. Steneker, Wijnand Differential Geometry Mathematical Physics Classical Analysis and ODEs Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler--Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational. |
| title | Variationality of conformal geodesics in dimension 3 |
| topic | Differential Geometry Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2412.04890 |