Sur la lin\'earisation des tissus

TL;DR

This paper provides an analytic criterion for linearizing 1-codimensional webs, interprets it geometrically via projective connections, and extends the approach to more general objects, illustrated with examples.

Contribution

It introduces a new analytic criterion for linearization of webs and links it to projective geometry, broadening the scope beyond 1-codimensional webs.

Findings

Analytic criterion characterizes linearizable webs

Geometric interpretation via projective connection

Extension to more general geometric objects

Abstract

We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study linearization of more general objects than 1-codimensional webs. By way of illustration, we treat some explicit interesting examples.