New characterization of vector field on Weil bundles

TL;DR

This paper introduces a new way to define and characterize vector fields on Weil bundles, which are geometric structures associated with smooth manifolds and Weil algebras.

Contribution

It provides an alternative definition and characterization of vector fields on Weil bundles, enhancing understanding of their geometric structure.

Findings

New characterization of vector fields on Weil bundles

Simplifies understanding of vector fields in this context

Potential applications in differential geometry and algebraic structures

Abstract

Let M be a paracompact smooth manifold, A a Weil algebra and M^A the associated Weil bundle. In this paper, we give another definition and characterization of vector field on M^A.