H. Weyl's and E. Cartan's proposals for infinitesimal geometry in the early 1920s

In the early phase of general relativity Elie Cartan and Hermann Weyl thought about the question of how the role of transformation groups could be transferred from classical geometry (Erlangen program) to differential geometry. They had different starting points and used different techniques, but both generalized the concept of connection arising from Levi-Civita's interpretation of the classical Christoffel symbols as parallel transfer in curved spaces. Their focus differed and Cartan headed toward a much more general framwork than Weyl (non-holonomous spaces versus scale gauge geometry). But there also was an overlap of topics (space problem) and, at the turn to the 1930s, they arrived at an agreement on how to deal with Cartan's infinitesimal geometric structures.