Correspondence Between Infinitesimal and Integral Description of Connections

摘要

We point out that there is no equivalence between infinitesimal (connection form or distribution of horizontal subspaces) and integral (path formalism) description of connections. There will be a one-to-one correspondence if the notion of (infinitesimal) connection is generalized. This is done by introducing ''infinitesimally non-linear'' connections. (Atomindex citation 14:747322)