  For Riemannian submersions, we establish some estimates for the spectrum of
the total space in terms of the spectrum of the base space and the geometry of
the fibers. In particular, for Riemannian submersions of complete manifolds
with closed fibers of bounded mean curvature, we show that the spectrum of the
base space is discrete if and only if the spectrum of the total space is
discrete.

Differential Geometry;Spectral Theory