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Kato constants in Riemannian geometry. (English) Zbl 1039.53033
The aim of this paper is to derive improvements of Kato’s inequality for sections of an irreducible SO(n)- or Spin(n)-bundle V over Riemannian manifolds under the assumption that the section solves a first-order equivariant (under SO(n) or Spin(n)) injectively elliptic system. An explicit general formula is given for the improved Kato constant.

MSC:
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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