  In the setting of step 2 sub-Finsler Carnot groups with strictly convex
norms, we prove that all infinite geodesics are lines. It follows that for any
other homogeneous distance, all geodesics are lines exactly when the induced
norm on the horizontal space is strictly convex. As a further consequence, we
show that all isometric embeddings between such homogeneous groups are affine.
The core of the proof is an asymptotic study of the extremals given by the
Pontryagin Maximum Principle.
