Torsion of $α$-connections on the density manifold
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912301184974848 |
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| author | Ay, Nihat Schwachhöfer, Lorenz J. |
| author_facet | Ay, Nihat Schwachhöfer, Lorenz J. |
| contents | We study the torsion of the $α$-connections defined on the density manifold in terms of a regular Riemannian metric. In the case of the Fisher-Rao metric our results confirm the fact that all $α$-connections are torsion free. For the $α$-connections obtained by the Otto metric, we show that, except for $α= -1$, they are not torsion free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion of $α$-connections on the density manifold Ay, Nihat Schwachhöfer, Lorenz J. Information Theory We study the torsion of the $α$-connections defined on the density manifold in terms of a regular Riemannian metric. In the case of the Fisher-Rao metric our results confirm the fact that all $α$-connections are torsion free. For the $α$-connections obtained by the Otto metric, we show that, except for $α= -1$, they are not torsion free. |
| title | Torsion of $α$-connections on the density manifold |
| topic | Information Theory |
| url | https://arxiv.org/abs/2503.23588 |