The norm of Cartan torsion plays an important role for studying of immersion theory in Finsler geometry. In this paper, we find necessary and sufficient condition under which a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold has bounded Cartan torsion.
1. S. B´acs´o, X. Cheng, and Z. Shen, Curvature properties of (α, β)-metrics, Adv. Stud. Pure. Math. Soc. Japan. 48(2007), 73-110.
2. D. Bao, S.S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, 2000.
3. D. Bao and S. S. Chern, A note on the Gauss-Bonnet theorem for Finsler spaces, Ann. Math. 143(1996), 233252.
4. L. Berwald, Uber die ¨ n-dimensionalen Geometrien konstanter Kr¨ummung, in denen die Geraden die k¨urzesten sind, Math. Z. 30(1929), 449-469.
5. D. Burago and S. Ivanov, Isometric embedding of Finsler manifolds, Algebra i Analiz, 5 (1993), 179-192.
6. E. Cartan, les spaces de Finsler. Actualites Scientifiques et industrilles, no. 79, Hermann, Paris, 1934.
7. X. Cheng, Z. Shen and Y. Tian, A class of Einstein (α, β)-metrics, Israel J. Math, 192(2012), 221-249.
8. P. Finsler, Uber Kurven und Fl¨achen in allgemeinen R¨aumen ¨ . Verlag Birkh¨auser, Basel, 1951.
9. R. S. Ingarden, Uber die Einbetting eines Finslerschen Rammes in einan Minkowskischen ¨ Raum, Bull. Acad. Polon. Sci. III, 2(1954), 305-308.
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. J. Nash, The imbedding problem for Riemannian manifolds, Ann. Math. 73(1957), 20-37.
13. T. 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.
14. Z. Shen, On a class of Landsberg metrics in Finsler geometry, Canadian. J. Math. 61(2009), 1357-1374.
15. Z. Shen, On Finsler geometry of submanifolds, Math. Ann. 311(1998), 549-576.
16. Z. Shen, On R-quadratic Finsler spaces, Publ. Math. Debrecen, 58(2001), 263-274.
17. Z. Shen, Projectively flat Finsler metrics of constant flag curvature, Trans. Amer. Math. Soc. 355(4) (2003), 1713-1728.
18. A. Tayebi and H. Sadeghi, On Cartan torsion of Finsler metrics, Publ. Math. Debrecen, 82(2013), 461-471.
19. A. Tayebi and H. Sadeghi, Two classes of Finsler metrics with bounded Cartan torsions, Global Journal. Advanced. Research. Classical. Modern Geometries, 7(1) (2018), 23-36.
20. G. Yang, On a class of singular Douglas and projectively flat Finsler metrics, Differ. Geom. Appl. 32(2014), 113-129.
21. G. Yang, On a class of singular projectively flat Finsler metrics with constant flag curvature, Int. J. Math. 24(2013), 16 pages, 1350087.
22. L. Zhou, A local classification of a class of (α, β)-metrics with constant flag curvature. Differ. Geom. Appl. 28(2010), 170-193
Sadeghi, H. (2021). Finsler metrics with bounded Cartan torsion. Journal of Finsler Geometry and its Applications, 2(1), 51-62. doi: 10.22098/jfga.2021.1263
MLA
Hassan Sadeghi. "Finsler metrics with bounded Cartan torsion", Journal of Finsler Geometry and its Applications, 2, 1, 2021, 51-62. doi: 10.22098/jfga.2021.1263
HARVARD
Sadeghi, H. (2021). 'Finsler metrics with bounded Cartan torsion', Journal of Finsler Geometry and its Applications, 2(1), pp. 51-62. doi: 10.22098/jfga.2021.1263
VANCOUVER
Sadeghi, H. Finsler metrics with bounded Cartan torsion. Journal of Finsler Geometry and its Applications, 2021; 2(1): 51-62. doi: 10.22098/jfga.2021.1263