The $\mathcal{C}$-connection and the 4-dimensional Einstein spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909327227355136 |
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| author | García-Parrado, Alfonso |
| author_facet | García-Parrado, Alfonso |
| contents | We introduce a new family of operators in 4-dimensional pseudo-Riemannian manifolds with a non-vanishing Weyl scalar (non-degenerate spaces) that keep the conformal covariance of \emph{conformally covariant tensor concomitants}. A particular case that arises naturally is the $\mathcal{C}$-connection that is a Weyl connection that keeps \emph{conformal invariance}. Using the $\mathcal{C}-$connection we give a new characterization of non-degenerate spaces that are conformal to an Einstein space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $\mathcal{C}$-connection and the 4-dimensional Einstein spaces García-Parrado, Alfonso Differential Geometry General Relativity and Quantum Cosmology We introduce a new family of operators in 4-dimensional pseudo-Riemannian manifolds with a non-vanishing Weyl scalar (non-degenerate spaces) that keep the conformal covariance of \emph{conformally covariant tensor concomitants}. A particular case that arises naturally is the $\mathcal{C}$-connection that is a Weyl connection that keeps \emph{conformal invariance}. Using the $\mathcal{C}-$connection we give a new characterization of non-degenerate spaces that are conformal to an Einstein space. |
| title | The $\mathcal{C}$-connection and the 4-dimensional Einstein spaces |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2409.17949 |