CLIFFORD–WOLF TRANSLATIONS OF LEFT INVARIANT RANDERS METRICS ON COMPACT LIE GROUPS

A Clifford–Wolf translation (CW-translation) of a connected Finsler space is an isometry which moves all points the same distance. A Finsler space (M, F) is called Clifford–Wolf homogeneous (CW-homogeneous) if, for any two points x1, x2 ∈ M, there is a CW-translation ρ such that ρ(x1) = x2. In this paper, we study CW-translations of left invariant Randers metrics on compact Lie groups. The main result is that a left invariant Randers metric on a compact, connected, simple Lie group is CW-homogeneous if and only if the indicatrix of the metric is a round sphere (not necessarily centered at the origin) with respect to a bi-invariant Riemannian metric. This presents a large number of examples of non-reversible Finsler metrics which are CW-homogeneous.