  In the present paper, we study the infinitesimal symmetries of the model of
two Riemannian manifolds $(M,g)$ and $(\hat M,\hat g)$ rolling without twisting
or slipping. We show that, under certain genericity hypotheses, the natural
bundle projection from the state space $Q$ of the rolling model onto $M$ is a
principal bundle if and only if $\hat M$ has constant sectional curvature.
Additionally, we prove that when $M$ and $\hat M$ have different constant
sectional curvatures and dimension $n\geq3$, the rolling distribution is never
flat, contrary to the two dimensional situation of rolling two spheres of radii
in the proportion $1\colon3$, which is a well-known system satisfying \'E.
Cartan's flatness condition.
