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Title: Homogeneous Randers spaces admitting just two homogeneous geodesics (English)
Author: Dušek, Zdeněk
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 55
Issue: 5
Year: 2019
Pages: 281-288
Summary lang: English
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Category: math
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Summary: The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented. (English)
Keyword: homogeneous space
Keyword: Finsler space
Keyword: Randers space
Keyword: homogeneous geodesic
MSC: 53C22
MSC: 53C30
MSC: 53C60
idZBL: Zbl 07144743
idMR: MR4057925
DOI: 10.5817/AM2019-5-281
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Date available: 2019-12-09T12:21:15Z
Last updated: 2020-11-24
Stable URL: http://hdl.handle.net/10338.dmlcz/147941
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Reference: [1] Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler Geometry.Springer Science+Business Media, New York, 2000. Zbl 0954.53001, MR 1747675
Reference: [2] Deng, S.: Homogeneous Finsler Spaces.Springer Science+Business Media, New York, 2012. MR 2962626
Reference: [3] Dušek, Z.: Geodesic graphs in homogeneous Randers spaces.Comment. Math. Univ. Carolinae, to appear.
Reference: [4] Dušek, Z.: The affine approach to homogeneous geodesics in homogeneous Finsler spaces.Arch. Math. (Brno) 54 (5) (2018), 257–263. MR 3887353, 10.5817/AM2018-5-257
Reference: [5] Dušek, Z.: The existence of homogeneous geodesics in special homogeneous Finsler spaces.Matematički Vesnik 71 (1–2) (2019), 16–22. MR 3895904
Reference: [6] Kowalski, O., Nikčević, S., Vlášek, Z.: Homogeneous geodesics in homogeneous Riemannian manifolds - Examples.Preprint Reihe Mathematik, TU Berlin, No. 665/2000. MR 1801906
Reference: [7] Kowalski, O., Szenthe, J.: On the existence of homogeneous geodesics in homogeneous Riemannian manifolds.Geom. Dedicata 84 (2001), 331–332. MR 1825363, 10.1023/A:1010308826374
Reference: [8] Kowalski, O., Vanhecke, L.: Riemannian manifolds with homogeneous geodesics.Boll. Un. Math. Ital. B (7) 5 (1991), 189–246. Zbl 0731.53046, MR 1110676
Reference: [9] Kowalski, O., Vlášek, Z.: Homogeneous Riemannian manifolds with only one homogeneous geodesic.Publ. Math. Debrecen 62 (3–4) (2003), 437–446. MR 2008107
Reference: [10] Latifi, D.: Homogeneous geodesics in homogeneous Finsler spaces.J. Geom. Phys. 57 (2007), 1421–1433. MR 2289656, 10.1016/j.geomphys.2006.11.004
Reference: [11] Yan, Z., Deng, S.: Finsler spaces whose geodesics are orbits.Diff. Geom. Appl. 36 (2014), 1–23. MR 3262894, 10.1016/j.difgeo.2014.06.006
Reference: [12] Yan, Z., Deng, S.: Existence of homogeneous geodesics on homogeneous Randers spaces.Houston J. Math. 44 (2) (2018), 481–493. MR 3845106
Reference: [13] Yan, Z., Huang, L.: On the existence of homogeneous geodesic in homogeneous Finsler spaces.J. Geom. Phys. 124 (2018), 264–267. MR 3754513, 10.1016/j.geomphys.2017.10.005
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