Gronwall's conjecture for 3-webs with infinitesimal symmetries

TL;DR

This paper proves Gronwall's conjecture for 3-webs with infinitesimal symmetries by classifying such webs and providing a linearization criterion using multi-dimensional Schwarzian derivatives.

Contribution

It offers a projective classification of non-flat planar 3-webs with infinitesimal symmetries and confirms Gronwall's conjecture in this specific case.

Findings

Gronwall's conjecture holds for 3-webs with infinitesimal symmetries

A new linearization criterion using multi-dimensional Schwarzian derivatives is established

A projective classification of these webs is provided

Abstract

We study non-flat planar 3-webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projective classification thereof. Using this classification we show that the Gronwall conjecture is true for 3-webs admitting infinitesimal symmetries.