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In the early phase of general relativity Elie Cartan and Hermann Weyl thoughtabout the question of how the role of transformation groups could betransferred from classical geometry (Erlangen program) to differentialgeometry. They had different starting points and used different techniques, butboth generalized the concept of connection arising from Levi-Civita'sinterpretation of the classical Christoffel symbols as parallel transfer incurved spaces. Their focus differed and Cartan headed toward a much moregeneral 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 the1930s, they arrived at an agreement on how to deal with Cartan's infinitesimalgeometric structures.

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