https://universite-paris-saclay.hal.science/hal-03286232Merker, JoëlJoëlMerkerLMO - Laboratoire de Mathématiques d'Orsay - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche ScientifiqueLie Symmetries and CR GeometryHAL CCSD2008[MATH] Mathematics [math]MERKER, Joël2021-07-17 21:48:192023-03-24 14:53:222021-07-19 08:41:52enJournal articleshttps://universite-paris-saclay.hal.science/hal-03286232/document10.1007/s10958-008-9201-5application/pdf1This paper is divided into three parts 1. Part I develops a general, new theory (inspired by modern CR geometry) of Lie symmetries of completely integrable pde systems, viewed from their associated submanifolds of solutions. Part II constructs general combinatorial formulas for the prolongations of vector fields to jet spaces. Part III explicitly characterizes the flatness of some systems of the second order. The results presented here are original and were not published elsewhere; most formulas of Parts II and III were verified by means of Maple Release 7.