  We present a simple method for proving Rellich inequalities on Riemannian
manifolds with constant, non-positive sectional curvature. The method is built
upon simple convexity arguments, integration by parts, and the so-called
Riccati pairs, which are based on the solvability of a Riccati-type ordinary
differential inequality. These results can be viewed as the higher order
counterparts of the recent work by Kaj\'ant\'o, Krist\'aly, Peter, and Zhao,
discussing Hardy inequalities using Riccati pairs.
