Refined Kato inequalities and conformal weights in Riemannian geometry

Abstract

We establish refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator. Our main result is a general expression which gives the value of the constants appearing in the refined inequalities. These constants are shown to be optimal and are computed explicitly in most practical cases.

AMS-LaTeX, 36pp, 1 figure (region.eps)