The natural reductivity in Finsler geometry in terms of geodesic graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908614066700288 |
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| author | Arias-Marco, Teresa Dusek, Zdenek |
| author_facet | Arias-Marco, Teresa Dusek, Zdenek |
| contents | A new geometrical definition of naturally reductive Finsler manifold using geodeic graph is proposed, with a possible generalization. Based on a construction from a recent paper by the authors, Finsler metrics based on naturally reductive Riemannian metrics $g_i$ are studied. Explicit examples of purely Finsler naturally reductive $α_i$-type metrics are constructed. Geodesic graphs on broad classes of Finsler $α_i$-type metrics $F$ which are derived from naturally reductive Riemannian metrics and which are not naturally reductive are described. The influence of one-forms $β_j$ to the structure of geodesics of the metric $F$ is also demonstrated and explicit construction of families of Finsler naturally reductive metrics of the $(α_i,β_j)$-type is described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The natural reductivity in Finsler geometry in terms of geodesic graphs Arias-Marco, Teresa Dusek, Zdenek Differential Geometry 53C22, 53C60, 53C30 A new geometrical definition of naturally reductive Finsler manifold using geodeic graph is proposed, with a possible generalization. Based on a construction from a recent paper by the authors, Finsler metrics based on naturally reductive Riemannian metrics $g_i$ are studied. Explicit examples of purely Finsler naturally reductive $α_i$-type metrics are constructed. Geodesic graphs on broad classes of Finsler $α_i$-type metrics $F$ which are derived from naturally reductive Riemannian metrics and which are not naturally reductive are described. The influence of one-forms $β_j$ to the structure of geodesics of the metric $F$ is also demonstrated and explicit construction of families of Finsler naturally reductive metrics of the $(α_i,β_j)$-type is described. |
| title | The natural reductivity in Finsler geometry in terms of geodesic graphs |
| topic | Differential Geometry 53C22, 53C60, 53C30 |
| url | https://arxiv.org/abs/2510.22687 |