Basic aspects of differential geometry

Marc Chaperon (1, 2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 UPCité - UFR Mathématiques - Université Paris Cité - UFR Mathématiques [Sciences]

This is a very partial description of differential geometry as elaborated by Élie Cartan and expressed in a suitable language by Charles Ehresmann. I am entirely responsable for the selection of materials and for the mistakes, if any. The framework is that of smooth (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 k th derivative of a map f is denoted by D^k f as in [10]. Paths are defined on intervals.

Domains: Mathematics [math]; Differential Geometry [math.DG]; Mathematics [math]; Analysis of PDEs [math.AP]

Marc Chaperon. Basic aspects of differential geometry. Geometry in History, Springer, 2019, ⟨10.1007/978-3-030-13609-3_15⟩. ⟨hal-03838511⟩