  In certain circumstances tools of Riemannian geometry are sufficient to
address questions arising in the more general Finslerian context. We show that
one such instance presents itself in the characterisation of geodesics in
Randers spaces of constant flag curvature. To achieve a simple, Riemannian
derivation of this special family of curves, we exploit the connection between
Randers spaces and the Zermelo problem of time-optimal navigation in the
presence of background fields. The characterisation of geodesics is then proven
by generalising an intuitive argument developed recently for the solution of
the quantum Zermelo problem.
