Ismail Kombe and Murad Ozaydin Improved Hardy and Rellich inequalities on Riemannian manifolds (278K, PDF) ABSTRACT. In this paper we establish improved Hardy and Rellich type inequalities on Riemannian manifold $M$. Furthermore, we also obtain sharp constant for the improved Hardy inequality and explicit constant for the Rellich inequality on hyperbolic space $\mathbb{H}^n$.