Document Type: Original Article
Department of Physical Sciences Landmark University, P. M. B. 1001, Omu-Aran, Kwara State, Nigeria
Department of Mathematics and Statistics, Osun State College of Technology, P. M. B. 1011, Nigeria
In this paper, we study the Hardy-Rellich type inequalities and uncertainty principle on the geodesic sphere. Firstly, we derive $L^p$-Hardy inequalities via divergence theorem, which are in turn used to establish the $L^p$ Rellich inequalities. We also establish Heisenberg uncertainty principle on the sphere via the Hardy-Rellich type inequalities. The best constants appearing in the inequalities are shown to be sharp.