Kato constants in Riemannian geometry

We derive improvements of Kato’s inequality for sections of an irreducible $\operatorname{SO}(n)$- or ${\rm Spin}(n)$-bundle $\mathbb{V}$ in the category of Riemannian manifolds, under the assumption that the section solves a first-order equivariant injectively elliptic system $\cD$. An explicit, general (covering all $\mathbb{V}$ and $\cal D$) formula is given for the improved Kato constant.

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Published 1 January 2000