Fréchet geometry via projective limits

Abstract

Fréchet spaces of sections arise naturally as configurations of a physical field. Some recent work in Fréchet geometry is briefly reviewed and some suggestions for future work are offered. An earlier result on the structure of second tangent bundles in the finite-dimensional case was extended to infinite-dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Fréchet structure needed for applications.