Homogeneous Randers spaces admitting just two homogeneous geodesics
Archivum Mathematicum (2019)
- Volume: 055, Issue: 5, page 281-288
- ISSN: 0044-8753
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topDušek, Zdeněk. "Homogeneous Randers spaces admitting just two homogeneous geodesics." Archivum Mathematicum 055.5 (2019): 281-288. <http://eudml.org/doc/294806>.
@article{Dušek2019,
abstract = {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.},
author = {Dušek, Zdeněk},
journal = {Archivum Mathematicum},
keywords = {homogeneous space; Finsler space; Randers space; homogeneous geodesic},
language = {eng},
number = {5},
pages = {281-288},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Homogeneous Randers spaces admitting just two homogeneous geodesics},
url = {http://eudml.org/doc/294806},
volume = {055},
year = {2019},
}
TY - JOUR
AU - Dušek, Zdeněk
TI - Homogeneous Randers spaces admitting just two homogeneous geodesics
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 5
SP - 281
EP - 288
AB - 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.
LA - eng
KW - homogeneous space; Finsler space; Randers space; homogeneous geodesic
UR - http://eudml.org/doc/294806
ER -
References
top- Bao, D., Chern, S.-S., Shen, Z., An Introduction to Riemann-Finsler Geometry, Springer Science+Business Media, New York, 2000. (2000) Zbl0954.53001MR1747675
- Deng, S., Homogeneous Finsler Spaces, Springer Science+Business Media, New York, 2012. (2012) MR2962626
- Dušek, Z., Geodesic graphs in homogeneous Randers spaces, Comment. Math. Univ. Carolinae, to appear.
- Dušek, Z., 10.5817/AM2018-5-257, Arch. Math. (Brno) 54 (5) (2018), 257–263. (2018) MR3887353DOI10.5817/AM2018-5-257
- Dušek, Z., The existence of homogeneous geodesics in special homogeneous Finsler spaces, Matematički Vesnik 71 (1–2) (2019), 16–22. (2019) MR3895904
- Kowalski, O., Nikčević, S., Vlášek, Z., Homogeneous geodesics in homogeneous Riemannian manifolds - Examples, Preprint Reihe Mathematik, TU Berlin, No. 665/2000. MR1801906
- Kowalski, O., Szenthe, J., 10.1023/A:1010308826374, Geom. Dedicata 84 (2001), 331–332. (2001) MR1825363DOI10.1023/A:1010308826374
- Kowalski, O., Vanhecke, L., Riemannian manifolds with homogeneous geodesics, Boll. Un. Math. Ital. B (7) 5 (1991), 189–246. (1991) Zbl0731.53046MR1110676
- Kowalski, O., Vlášek, Z., Homogeneous Riemannian manifolds with only one homogeneous geodesic, Publ. Math. Debrecen 62 (3–4) (2003), 437–446. (2003) MR2008107
- Latifi, D., 10.1016/j.geomphys.2006.11.004, J. Geom. Phys. 57 (2007), 1421–1433. (2007) MR2289656DOI10.1016/j.geomphys.2006.11.004
- Yan, Z., Deng, S., 10.1016/j.difgeo.2014.06.006, Diff. Geom. Appl. 36 (2014), 1–23. (2014) MR3262894DOI10.1016/j.difgeo.2014.06.006
- Yan, Z., Deng, S., Existence of homogeneous geodesics on homogeneous Randers spaces, Houston J. Math. 44 (2) (2018), 481–493. (2018) MR3845106
- Yan, Z., Huang, L., 10.1016/j.geomphys.2017.10.005, J. Geom. Phys. 124 (2018), 264–267. (2018) MR3754513DOI10.1016/j.geomphys.2017.10.005
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