Affine Classification of n-Curves

TL;DR

This paper develops exact formulas for affine invariants of n-curves, providing a complete classification method based on Cartan's lemma and affine equivalence, advancing the mathematical understanding of curve classification.

Contribution

It introduces a novel approach to classify n-curves using explicit affine invariants derived from Cartan's lemma, offering a necessary and sufficient condition for classification.

Findings

Derived exact formulas for affine invariants of n-curves

Established a necessary and sufficient condition for affine classification

Provided a new mathematical framework for curve equivalence under affine transformations

Abstract

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartan's lemma and then, state a necessary and sufficient condition for classification of n--Curves.