Differential Geometry of Microlinear Frolicher Spaces II

TL;DR

This paper develops a geometric characterization of exterior differentiation within microlinear Frolicher spaces, filling a gap in orthodox differential geometry by establishing its unique infinitesimal definition.

Contribution

It introduces a geometric approach to defining exterior differentiation, extending the differential geometry of microlinear Frolicher spaces.

Findings

Exterior differentiation is uniquely determined geometrically.

Provides an infinitesimal characterization of exterior differentiation.

Fills a gap in classical differential geometry theory.

Abstract

In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometrically or physically in classical vector calculus. This infinitesimal characterization of exterior differentiation has been completely missing in orthodox differential geometry.