Abstract: The symmetry of space time is described by using the so called isometric group. The generators of isometric group are directly connected with the Killing vectors. In this paper, we present an explicit connection between the symmetries in the VSR and isometric group of Finsler space. The Killing vectors in Finsler space are constructed in a systematic way. Further, the solutions of Killing equations are present explicitly in the isometric symmetry of Finsler spaces. The Killing vectors of Finsler-Berwald space are given and we proved that the 4-dimensional Finsler-Berwald space with constant curvature has 15 independent Killing vectors.
Keywords: Finsler-Berwald space, very special relativity, Killing vectors, Lorentz violation, isometric group.
Classification (MSC2000): 53B40; 53C60, 58J60
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