The Existence of Two Homogeneous Geodesics in Finsler Geometry
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved....
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/7/850 |
| _version_ | 1798024682367090688 |
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| author | Zdeněk Dušek |
| author_facet | Zdeněk Dušek |
| author_sort | Zdeněk Dušek |
| collection | DOAJ |
| description | The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible. |
| first_indexed | 2024-04-11T18:06:36Z |
| format | Article |
| id | doaj.art-97a4003bb4d3486288e44edce671b9bf |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T18:06:36Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-97a4003bb4d3486288e44edce671b9bf2022-12-22T04:10:18ZengMDPI AGSymmetry2073-89942019-07-0111785010.3390/sym11070850sym11070850The Existence of Two Homogeneous Geodesics in Finsler GeometryZdeněk Dušek0Institute of Technology and Business in České Budějovice, Okružní 517/10, 370 01 České Budějovice, Czech RepublicThe existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.https://www.mdpi.com/2073-8994/11/7/850homogeneous manifoldhomogeneous Finsler spacehomogeneous geodesic |
| spellingShingle | Zdeněk Dušek The Existence of Two Homogeneous Geodesics in Finsler Geometry Symmetry homogeneous manifold homogeneous Finsler space homogeneous geodesic |
| title | The Existence of Two Homogeneous Geodesics in Finsler Geometry |
| title_full | The Existence of Two Homogeneous Geodesics in Finsler Geometry |
| title_fullStr | The Existence of Two Homogeneous Geodesics in Finsler Geometry |
| title_full_unstemmed | The Existence of Two Homogeneous Geodesics in Finsler Geometry |
| title_short | The Existence of Two Homogeneous Geodesics in Finsler Geometry |
| title_sort | existence of two homogeneous geodesics in finsler geometry |
| topic | homogeneous manifold homogeneous Finsler space homogeneous geodesic |
| url | https://www.mdpi.com/2073-8994/11/7/850 |
| work_keys_str_mv | AT zdenekdusek theexistenceoftwohomogeneousgeodesicsinfinslergeometry AT zdenekdusek existenceoftwohomogeneousgeodesicsinfinslergeometry |