Differential Geometry of Microlinear Frolicher Spaces IV-2

TL;DR

This paper advances the differential geometry of microlinear Frölicher spaces by establishing affine bundle theorems for jet bundles and demonstrating the equivalence of three approaches in coordinate contexts.

Contribution

It introduces affine bundle theorems for second and third jet bundle approaches and proves their equivalence when coordinates are available.

Findings

Affine bundle theorems for second and third approaches

Equivalence of three jet bundle approaches in coordinate settings

Comparison of different jet bundle methodologies

Abstract

This paper is the sequel to our previous paper (Differetial Geometry of Microlinear Frolicher spaces IV-1), where three approaches to jet bundles are presented and compared. The first objective in this paper is to give the affine bundle theorem for the second and third approaches to jet bundles. The second objective is to deal with the three approaches to jet bundles in the context where coordinates are available. In this context all the three approaches are shown to be equivalent.