BASIC ASPECTS OF DIFFERENTIAL GEOMETRY
This is a very partial description of differential geometry as elaborated by Elie Cartan and expressed in a suitable language by Charles Ehresmann. As this new language has become classical, I apologize to those who know it better than myself: this text is not written for them. I am entirely responsable for the selection of materials and for the mistakes, if any. The framework is that of smooth1 (finite dimensional) manifolds and maps, whose definition is taken for granted—most of the notions we consider “pass” without any problem to the real analytic and (replacing R by C) complex and/or Banach categories. The kth derivative of a map f is denoted by Dkf as in [10]. Paths are defined on intervals.