In this paper we consider invariant square metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces. We study geodesic vectors and investigates the set of all homogeneous geodesics on two-step nilpotent Lie groups of dimension five.
1. H. An and S. Deng, Ivariant (α,β)-metric on homogeneous manifolds, Monatsh. Math., 154(2008), 89-102.
2. D. Bao, S. S. Chern and Z. Shen, An introduction to Riemann-Finsler geometry, SpringerVerlag, (2000).
3. S. S. Chern and Z. Shen, Riemann-Finsler geometry, World Scientific, Nankai Tracts in Mathematics, (2005).
4. Z. Duˇsek, The existence of homogeneous geodesics in special homogeneous Finsler spaces, Matematicki Vesnik, 71(2019), 16-22.
5. Z. Duˇsek, The affine approach to homogeneous geodesics in homogeneous Finsler spaces, Archivum Mathematicum, 54(2018), 257- 263.
6. P. Eberlein, Geometry of 2-step nilpotent groups with a left invariant metric, Ann. Sci. Ecole Norm. Sup., 27(1994), 805-828.
7. P. Habibi and D. Latifi and M. Toomanian, Homogeneous geodesics and the critical points of the restricted Finsler function, J. Contem. Math. Anal. 46(2011), 12-16.
8. S. Homolya and O. Kowalski, Simply connected two-step homogeneous nilmanifolds of dimension 5, Note di Matematica, 1(2006), 69-77.
9. O. Kowalski and L. Vanhecke, Riemannian manifolds with homogeneous geodesics, Boll. Unione. Mat. Ital, 5(1991), 189-246.
10. D. Latifi, Homogeneous geodesics in homogeneous Finsler spaces, J. Geom. Phys., 57(2007), 1421-1433.
11. J. Lauret, Homogeneous nilmanifolds of dimensions 3 and 4, Geometriae Dedicata, 68(1997), 145-155.
12. M. Parhizkar and D. Latifi, Geodesic vectors of Randers metrics on nilpotent Lie groups of dimension five, Global. J. Adv. Res. Class. Moder. Geom. 7(2018), 92-101.
13. H. R. Salimi Moghaddam, On the Randers metrics on two-step homogenous nilmanifolds of dimention five, Int. J. Geom. Meth. Mod. Phys. 8(3) (2011) 501-510.
14. H. R. Salimi Moghaddam H. Abedi Karimi and M. Nasehi, Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups, Journal of Finsler Geometry and its Applications, 1(2) (2020), 15-26.
15. Z. Shen and G. C. Yildirim, On a class of projectively flat metrics with constant flag curvature, Canadian Journal of Mathematics, 60(2)(2008), 443-456.
16. A. Toth and Z. Kovacs, On the geometry of two-step nilpotent group with left invariant Finsler metrics, Acta. Math. Acad. Paedagogicae. Nyregyhaziensis., 24(2008) 155-168.
17. E. Wilso, Isometry groups on homogeneous nilmanifolds, Geometriae Dedicata, 12(1982), 337-346.
18. Z. Yan and L. Huang, On the existence of homogeneous geodesic in homogeneous Finsler spaces, J. Geom. Phys. 124(2018), 264-267.
19. Z. Yan and S. Deng, Finsler spaces whose geodesics ore orbits, Diff. Geom, Appl. 36(2014), 1-23.
20. Z. Yan, Some Finsler spaces with homogeneous geodesics, Math. Nach. 290(2017), 474- 481.
21. L. Zhou, A local classification of a class of (α,β)-metrics with constant flag curvature, Differ. Geom. Appl. 28(2010), 170-193.
Habibi, P. (2021). Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five. Journal of Finsler Geometry and its Applications, 2(1), 132-141. doi: 10.22098/jfga.2021.1270
MLA
Parastoo Habibi. "Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five", Journal of Finsler Geometry and its Applications, 2, 1, 2021, 132-141. doi: 10.22098/jfga.2021.1270
HARVARD
Habibi, P. (2021). 'Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five', Journal of Finsler Geometry and its Applications, 2(1), pp. 132-141. doi: 10.22098/jfga.2021.1270
VANCOUVER
Habibi, P. Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five. Journal of Finsler Geometry and its Applications, 2021; 2(1): 132-141. doi: 10.22098/jfga.2021.1270