Some Hardy and Rellich type inequalities for affine connections

Abstract

In this article we study various forms of the Hardy inequality for affine connections on a complete noncompact Riemannian manifold, including the two-weight Hardy inequality, the improved Hardy inequality, the Rellich inequality, the Hardy–Poincaré inequality and the Heisenberg–Pauli–Weyl inequality. Our results improve and include many previously known results as special cases.