Parall\'elisme d'une vari\'et\'e des points proches

TL;DR

This paper explores the concept of parallelism on A-manifolds, specifically on the manifold of near points, by analyzing the module structure of vector fields and establishing equivalence conditions.

Contribution

It introduces a new approach to understanding parallelism on A-manifolds using the module structure of vector fields on the manifold of near points.

Findings

Established the equivalence of parallelism on A-manifolds

Utilized the structure of C^{}(M^{A},A)-modules

Provided a framework for analyzing near points on manifolds

Abstract

Let M be a smooth manifold, A a local algebra, M^{A} the manifold of near points on M of kind A. We use the structure of C^{\infty}(M^{A},A)-module on the set X(M^{A}) of vector fields on M^{A} for to give the equivalence of parallelism of the A-manifold M^{A}.