  In this paper, we provide conceptional explanations for the geodesic and
Jacobi field correspondences for homothetic navigation, and then let them guide
us to the shortcuts to some well known flag curvature and S-curvature formulas.
They also help us directly see the local correspondence between isoparametric
functions or isoparametric hypersurfaces, which generalizes the classification
works of Q. He and her coworkers for isoparametric hypersurfaces in Randers
space forms and Funk spaces.
