Hardy-Poincar\'e, Rellich and Uncertainty principle inequalities on   Riemannian manifolds
  We continue our previous study of improved Hardy, Rellich and Uncertainty principle inequalities on a Riemannian manifold $M$, started in \cite{Kombe-Ozaydin}.   In the present paper we prove new weighted Hardy-Poincar\'e, Rellich type inequalities as well as improved version of our Uncertainty principle inequalities on a Riemannian manifold $M$. In particular, we obtain sharp constants for these inequalities on the hyperbolic space $\mathbb{H}^n$. 
Ismail Kombe, Murad \"Ozaydin
math.FA