For a second order operator on a compact manifold satisfying the strong
H\"ormander condition, we give a bound for the spectral gap analogous to the
Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a
wide class of such operators which includes horizontal lifts of the Laplacian
on Riemannian submersions with minimal leaves.Comment: 13 pages. To appear in Proceedings of the AM
