Communications in Analysis and Geometry

Volume 28 (2020)

Number 3

Gronwall’s conjecture for $3$-webs with infinitesimal symmetries

Pages: 519 – 545



Sergey I. Agafonov (Department of Mathematics, São Paulo State University – UNESP, São José do Rio Preto, Brazil)


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.

Received 6 November 2014

Accepted 10 January 2018

Published 6 July 2020