La formule de la trace pour les tissus planaires

TL;DR

This paper proves that for planar d-webs with d>3, the trace of the curvature of the associated connection equals the sum of the Blaschke curvatures of its 3-web substructures, providing a comprehensive mathematical validation.

Contribution

It offers a complete proof of a fundamental relation between curvature trace and Blaschke curvatures in planar d-webs, clarifying their geometric structure.

Findings

The trace of the curvature equals the sum of Blaschke curvatures for d-webs.

Provides a rigorous proof for the relation in planar webs with d>3.

Enhances understanding of geometric properties of planar webs.

Abstract

We give a complete proof of the fact that the trace of the curvature of the connection associated to a planar d-web (d>3) is the sum of the Blaschke curvatures of its sub 3-webs.