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

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