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

Rellich inequalities via Riccati pairs on model space forms