  If $\pi :M\rightarrow B$ is a Riemannian Submersion and $M$ has positive
sectional curvature, O'Neill's Horizontal Curvature Equation shows that $B$
must also have positive curvature. We show there are Riemannian submersions
from compact manifolds with positive Ricci curvature to manifolds that have
small neighborhoods of (arbitrarily) negative Ricci curvature, but that there
are no Riemannian submersions from manifolds with positive Ricci curvature to
manifolds with nonpositive Ricci curvature.
