  By further developing the generalized $\Gamma$-calculus for hypoelliptic
operators, we prove hypocoercive estimates for a large class of Kolmogorov type
operators which are defined on non necessarily totally geodesic Riemannian
foliations. We study then in detail the example of the velocity spherical
Brownian motion, whose generator is a step-3 generating hypoelliptic
H\"ormander's type operator. To prove hypocoercivity in that case, the key
point is to show the existence of a convenient Riemannian foliation associated
to the diffusion. We will then deduce, under suitable geometric conditions, the
convergence to equilibrium of the diffusion in $H^1$ and in $L^2$.
