  We prove some estimates on the spectrum of the Laplacian of the total space
of a Riemannian submersion in terms of the spectrum of the Laplacian of the
base and the geometry of the fibers. When the fibers of the submersions are
compact and minimal, we prove that the total space is discrete if and only if
the base is discrete. When the fibers are not minimal, we prove a discreteness
criterion for the total space in terms of the relative growth of the mean
curvature of the fibers and the mean curvature of the geodesic spheres in the
base. We discuss in particular the case of warped products.
