The relation between automorphism group and isometry group of left invariant (α, β)-metrics

Salimi Moghaddam, Hamid Reza; Nejadahmad, Masumeh

doi:10.22098/jfga.2023.12784.1088

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	The relation between automorphism group and isometry group of left invariant (α, β)-metrics
Journal of Finsler Geometry and its Applications
دوره 4، شماره 1، مهر 2023، صفحه 81-87 اصل مقاله (304.12 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2023.12784.1088
نویسندگان
Hamid Reza Salimi Moghaddam^* ¹؛ Masumeh Nejadahmad²
¹Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441-Iran.
²Department of Mathematics, Isfahan University of Technology, Iran.
چکیده
Let F be an (α,β)-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group G. We consider the automorphism and isometry groups of the Finsler manifold (G,F) and their intersection. We prove that for an arbitrary left invariant vector field X and any compact subgroup K of automorphisms which X is invariant under them, there exists an (α,β)-metric such that K is a subgroup of its isometry group.
کلیدواژه‌ها
Automorphism group؛ Isometry group؛ Lie group؛ Left Invariant (α؛ β)-metric

اصل مقاله

مراجع
1. P. L. Antonelli, R. S. Ingarden, M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer, Dordrecht, 1993. 2. G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories, D. Reidel, Dordrecht, 1985. 3. D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, 2000. 4. S. S. Chern and Z. Shen, Riemanian-Finsler Geometry, World Scientific, Singapore, 2005. 5. S. Deng, Homogeneous Finsler Spaces, Springer, New York, 2012. 6. S. Deng, M. Hosseini, H. Liu and H. R. Salimi Moghaddam, On left invariant (α, β)- metrics on some Lie groups, Houston J. Math. 45(4)(2019), 1071-1088. 7. S. Deng and Z. Hou, Invariant Randers metrics on homogeneous Riemannian manifolds, J. Phys. A: Math. Gen. 37(2004), 4353-4360. 8. S. Deng and Z. Hu, On flag curvature of homogeneous Randers spaces, Canad. J. Math. 65(1)(2013), 66-81. 9. P. Eberlein, Left invariant geometry of Lie groups, Cubo 6(1)(2004), 427-510. 10. E. Esrafilian and H. R. Salimi Moghaddam, Induced invariant Finsler metrics on quotient groups, Balkan J. Geom. Appl. 11(1)(2006), 73-79. 11. R. S. Ingarden, On physical applications of Finsler geometry, Contemp. Math. 196(1996), 213-223. 12. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry Vol. 2, Interscience Publishers, John Wiley & Sons, 1969. 13. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Addison-Wesley, Reading, 1962. 14. J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. Math. 21(1976), 293-329. 15. K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76(1954), 33-65. 16. H. R. Salimi Moghaddam, The relation between automorphism group and isometry group of Randers Lie groups, Results Math. 61(2012), 137-142.
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The relation between automorphism group and isometry group of left invariant (α, β)-metrics