Z. Shen proved that Finsler manifold with unbounded Cartan torsion can not be isometrically imbedded into any Minkowski space. This shows that the norm of Cartan torsion of Finsler metrics has an essential role for studying of immersion theory in Finsler geometry. In this paper, we study the norm of Cartan torsion of Ingarden-Tàmassy and Arctangent Finsler metrics that are special (α, β)-metrics.
1. D. Bao, S.S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, 2000.
2. D. Bao, C. Robles and Z. Shen, Zermelo navigation on Riemannian manifolds, J. Differential Geometry, 66(2004), 377-435.
3. D. Burago and S. Ivanov, Isometric embedding of Finsler manifolds, Algebra. Analiz. 5(1993), 179-192.
4. E. Cartan, Les espaces de Finsler, Actualit´es 79, Paris, 1934.
5. P. Finsler, Uber Kurven und Fl¨achen in allgemeinen R¨aumen ¨ , (Dissertation, G¨ottingan, 1918), Birkh¨auser Verlag, Basel, 1951.
6. C.H. Gu, Imbedding of a Finsler manifold in a Minkowski space, Acta. Math. Sinica. 7(1957), 215-232.
7. C.H. Gu, Imbedding of a Finsler manifold in a Minkowski space, Acta. Math. Sinica. 8(1958), 282-285.
8. R. S. Ingarden, Uber die Einbetting eines Finslerschen Rammes in einan Minkowskischen ¨ Raum, Bull. Acad. Polon. Sci. 2(1954), 305-308.
9. R. S. Ingarden and L. Tam´assy, The point Finsler spaces and their physical applications in electron optics and thermodynamics, Math. Comput. Modelling, 20(1994), 93-107.
10. M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys. 31(1992), 43-84.
11. X. Mo and L. Zhou, A class of Finsler metrics with bounded Cartan torsion, Canad. Math. Bull. 53(2010), 122-132.
12. G. Randers, On an asymmetric metric in the four-space of general relativity, Phys. Rev. 59(1941), 195-199.
13. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.
14. Z. Shen, On R-quadratic Finsler spaces, Publ. Math. Debrecen. 58(2001), 263-274.
15. Z. Shen, On Finsler geometry of submanifolds, Math. Ann. 311(3)(1998), 549-576. 1357- 1374.
16. Z. Shen and G. C. Yildirim, On a class of projectively flat metrics, Canadian Journal of Mathematics. 60(2008), 443-456,
17. A. Tayebi and H. Sadeghi, On Cartan torsion of Finsler metrics, Publ. Math. Debrecen. 82(2) (2013), 461-471.
18. A. Tayebi and H. Sadeghi, Two classes of Finsler metrics with bounded Cartan torsions, Global J. Adv. Res. Class. Mod. Geom. 7(1) (2018), 23-36.
Rajabi, T. (2020). On the norm of Cartan torsion of two classes of (α, β)−metrics. Journal of Finsler Geometry and its Applications, 1(1), 66-72. doi: 10.22098/jfga.2020.1012
MLA
Tahere Rajabi. "On the norm of Cartan torsion of two classes of (α, β)−metrics", Journal of Finsler Geometry and its Applications, 1, 1, 2020, 66-72. doi: 10.22098/jfga.2020.1012
HARVARD
Rajabi, T. (2020). 'On the norm of Cartan torsion of two classes of (α, β)−metrics', Journal of Finsler Geometry and its Applications, 1(1), pp. 66-72. doi: 10.22098/jfga.2020.1012
VANCOUVER
Rajabi, T. On the norm of Cartan torsion of two classes of (α, β)−metrics. Journal of Finsler Geometry and its Applications, 2020; 1(1): 66-72. doi: 10.22098/jfga.2020.1012
)