In this paper, we consider invariant infinite series (α, β)--metrics. Then we describe all geodesic vectors of this spaces on the left invariant hypercomplex four dimensional simply connected Lie groups.
1. P. Bahmandoust, D. Latifi, Naturally reductive homogeneous (α, β)-spaces, Int. J. Geom. Methods Mod. Phys., 17(8) (2020), 2050117.
2. D. Bao, S. S. Chern, Z. Shen, An introduction to Riemann-Finsler geometry, SpringerVerlage, 2000.
3. M. L. Barberis, Hypercomplex structures on four-dimensional Lie groups, Proc. Am. Math. Soc., 125(1997), 1043-1054.
4. M. Ebrahimi, D. Latifi, On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r, Journal of Lie Theory, 29(2019), 619-627.
5. S. Kobayashi and K. Nomizu, Foundations of differential Geometry, Interscience Publishers, (1969).
6. O. Kowalski, J. Szenthe, On the Existence of Homogeneous Geodesics in Homogeneous Riemannian manifolds, Geom. Dedicata, 81(2000), 209-214.
7. D. Latifi,Homogeneous geodesics in homogeneous Finsler spaces, J. Geom. Phys., 57(2007), 1421–1433.
8. D. Latifi, M. Toomanian, Invariant naturally reductive Randers metrics on homogeneous spaces, Math Sci, 6(63) (2012), 1-5.
9. D. Latifi, M. Toomanian, On the existence of bi-invariant Finsler metrics on Lie groups, Math Sci, 7(37) (2013), 1-5.
10. D. Latifi, Bi-invariant (α, β)-metrics on Lie groups, Acta Universitatis Apulensis, 65, (2021), 121-131.
11. M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys., 31(1992), 33–65.
12. M. Obata, Affine connections on manifolds with almost complex, quaternion or Hermitian structure, Jap. J. Math, 26(1956), 43-79.
13. M. Parhizkar, 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.
14. M. L. Zeinali, On generalized symmetric Finsler spaces with some special (α, β) -metrics, Journal of Finsler Geometry and its Applications, 1(1), (2020), 45-53.
Zeinali Laki, M. (2023). Geodesic vectors of infinite series (α, β)-metric on hypercomplex four dimensional Lie groups. Journal of Finsler Geometry and its Applications, 4(2), 103-112. doi: 10.22098/jfga.2023.14025.1107
MLA
Milad Zeinali Laki. "Geodesic vectors of infinite series (α, β)-metric on hypercomplex four dimensional Lie groups", Journal of Finsler Geometry and its Applications, 4, 2, 2023, 103-112. doi: 10.22098/jfga.2023.14025.1107
HARVARD
Zeinali Laki, M. (2023). 'Geodesic vectors of infinite series (α, β)-metric on hypercomplex four dimensional Lie groups', Journal of Finsler Geometry and its Applications, 4(2), pp. 103-112. doi: 10.22098/jfga.2023.14025.1107
VANCOUVER
Zeinali Laki, M. Geodesic vectors of infinite series (α, β)-metric on hypercomplex four dimensional Lie groups. Journal of Finsler Geometry and its Applications, 2023; 4(2): 103-112. doi: 10.22098/jfga.2023.14025.1107