Isometric group of (α,β)-type Finsler space and the symmetry of Very Special Relativity

2010/01/15 by Xin Li, Li, Xin, Zhe Chang +3
Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.1001.2667

openalex publication_date 2010/01/15 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The Killing equation for a general Finsler space is set up. It is showed that the Killing equation of (α,β) space can be divided into two parts. One is the same with Killing equation of a Riemannian metric, another equation can be regarded as a constraint. The solutions of Killing equations present explicitly the isometric symmetry of Finsler space. We find that the isometric group of a special case of (α,β) space is the same with the symmetry of Very Special Relativity (VSR). The Killing vectors of Finsler-Funk space are given. Unlike Riemannian constant curvature space, the 4 dimensional Funk space with constant curvature just have 6 independent Killing vectors.

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