Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
homogeneous space; Finsler space; Randers space; homogeneous geodesic
homogeneous space; Finsler space; Randers space; homogeneous geodesic
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.
References:
[1] Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler Geometry. Springer Science+Business Media, New York, 2000. MR 1747675 | Zbl 0954.53001
[2] Deng, S.: Homogeneous Finsler Spaces. Springer Science+Business Media, New York, 2012. MR 2962626
[3] Dušek, Z.: Geodesic graphs in homogeneous Randers spaces. Comment. Math. Univ. Carolinae, to appear.
[4] Dušek, Z.: The affine approach to homogeneous geodesics in homogeneous Finsler spaces. Arch. Math. (Brno) 54 (5) (2018), 257–263. DOI 10.5817/AM2018-5-257 | MR 3887353
[5] Dušek, Z.: The existence of homogeneous geodesics in special homogeneous Finsler spaces. Matematički Vesnik 71 (1–2) (2019), 16–22. MR 3895904
[6] Kowalski, O., Nikčević, S., Vlášek, Z.: Homogeneous geodesics in homogeneous Riemannian manifolds - Examples. Preprint Reihe Mathematik, TU Berlin, No. 665/2000. MR 1801906
[7] Kowalski, O., Szenthe, J.: On the existence of homogeneous geodesics in homogeneous Riemannian manifolds. Geom. Dedicata 84 (2001), 331–332. DOI 10.1023/A:1010308826374 | MR 1825363
[8] Kowalski, O., Vanhecke, L.: Riemannian manifolds with homogeneous geodesics. Boll. Un. Math. Ital. B (7) 5 (1991), 189–246. MR 1110676 | Zbl 0731.53046
[9] Kowalski, O., Vlášek, Z.: Homogeneous Riemannian manifolds with only one homogeneous geodesic. Publ. Math. Debrecen 62 (3–4) (2003), 437–446. MR 2008107
[10] Latifi, D.: Homogeneous geodesics in homogeneous Finsler spaces. J. Geom. Phys. 57 (2007), 1421–1433. DOI 10.1016/j.geomphys.2006.11.004 | MR 2289656
[11] Yan, Z., Deng, S.: Finsler spaces whose geodesics are orbits. Diff. Geom. Appl. 36 (2014), 1–23. DOI 10.1016/j.difgeo.2014.06.006 | MR 3262894
[12] Yan, Z., Deng, S.: Existence of homogeneous geodesics on homogeneous Randers spaces. Houston J. Math. 44 (2) (2018), 481–493. MR 3845106
[13] Yan, Z., Huang, L.: On the existence of homogeneous geodesic in homogeneous Finsler spaces. J. Geom. Phys. 124 (2018), 264–267. DOI 10.1016/j.geomphys.2017.10.005 | MR 3754513
Search
Partner of
