  In this paper we obtain Hardy, weighted Trudinger-Moser and
Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian
manifolds with non-positive sectional curvature and, in particular, a variety
of new estimates on hyperbolic spaces. Moreover, in some cases we also show
their equivalence with Trudinger-Moser inequalities. As consequences, the
relations between the constants of these inequalities are investigated yielding
asymptotically best constants in the obtained inequalities. We also obtain the
corresponding uncertainty type principles.
