Notions of affinity in calculus of variations with differential forms

TL;DR

This paper characterizes a class of affine functions in the calculus of variations involving differential forms, focusing on their affine properties with respect to exterior and interior products.

Contribution

It provides a characterization theorem for one affine functions in the calculus of variations with differential forms, advancing understanding of their structure.

Findings

Characterization theorem for one affine functions.

Clarification of affine properties in differential forms.

Implications for calculus of variations with differential forms.

Abstract

Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to prove a characterization theorem for this class of functions, which plays an important role in the calculus of variations for differential forms.