Structure of geodesics for Finsler metrics arising from Riemannian g.o. metrics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914847363432448 |
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| author | Arias-Marco, Teresa Dusek, Zdenek |
| author_facet | Arias-Marco, Teresa Dusek, Zdenek |
| contents | Homogeneous geodesics of homogeneous Finsler metrics derived from two or more Riemannian geodesic orbit metrics are investigated. For a broad newly defined family of positively related Riemannian geodesic orbit metrics, geodesic lemma is proved and it is shown that the derived Finsler metrics have also geodesic orbit property. These Finsler metrics belong to the newly defined class of the $α_i$-type metrics which includes in particular the $(α_1,α_2)$ metrics. Geodesic graph for the sphere ${\mathrm{S}}^7={\mathrm{Sp(2)}}{\mathrm{U}}(1)/{\mathrm{Sp(1)}{\mathrm{diag}}{\mathrm{U}}(1)}$ with geodesic orbit Finsler metrics of the new type $(α_1,α_2,α_3)$, arising from two or more Riemannian geodesic orbit metrics, is analyzed in detail. This type of metrics on $S^7$ is one of the missing cases in a previously published classification of geodesic orbit metrics on spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure of geodesics for Finsler metrics arising from Riemannian g.o. metrics Arias-Marco, Teresa Dusek, Zdenek Differential Geometry 53C22, 53C60, 53C30 Homogeneous geodesics of homogeneous Finsler metrics derived from two or more Riemannian geodesic orbit metrics are investigated. For a broad newly defined family of positively related Riemannian geodesic orbit metrics, geodesic lemma is proved and it is shown that the derived Finsler metrics have also geodesic orbit property. These Finsler metrics belong to the newly defined class of the $α_i$-type metrics which includes in particular the $(α_1,α_2)$ metrics. Geodesic graph for the sphere ${\mathrm{S}}^7={\mathrm{Sp(2)}}{\mathrm{U}}(1)/{\mathrm{Sp(1)}{\mathrm{diag}}{\mathrm{U}}(1)}$ with geodesic orbit Finsler metrics of the new type $(α_1,α_2,α_3)$, arising from two or more Riemannian geodesic orbit metrics, is analyzed in detail. This type of metrics on $S^7$ is one of the missing cases in a previously published classification of geodesic orbit metrics on spheres. |
| title | Structure of geodesics for Finsler metrics arising from Riemannian g.o. metrics |
| topic | Differential Geometry 53C22, 53C60, 53C30 |
| url | https://arxiv.org/abs/2406.16736 |