Feuilletage canonique sur le fibr\'e de Weil

TL;DR

This paper constructs the canonical foliation on the manifold of infinitely near points of a smooth manifold and relates it to the canonical foliation on the tangent bundle, providing a geometric framework.

Contribution

It introduces a canonical foliation on the manifold of infinitely near points and links it to the tangent bundle's canonical foliation, extending geometric understanding.

Findings

Canonical foliation on M^A is constructed.

Relation established between foliation on M^A and tangent bundle TM.

Provides geometric insights into manifolds of near points.

Abstract

Let be M a smooth manifold, A a local algebra and M^{A} a manifold of infinitely near points on M of kind A. We build the canonical foliation on M^{A} et we show that the canonical foliation on the tangent bundle TM is the foliation defined by his canonical field.