Non-holonomic connections following Élie Cartan (Q2731762)

Not in any case it is an easy task to transmit an older investigation in differential geometry or analytic mechanics to modern terms. With this aim the authors' project is to revisit E. Cartans's adress at the 1928 International Congress of Mathematicians [Proc. Int. Cong. Math. Bologna, 4, 253-261]. Introducing the notion of strongly or maximally nonholonomic connections, they interpret Cartan's text thoroughly, though they have to admit not being able to decipher each of Cartan's arguments. Some generalizations of Cartan's notions and results concerning the so-called \(E\)-restricted connections are given, where \(E\) is a subbundle of the tangent bundle of a smooth manifold.