LINKS BETWEEN CONNECTIONS, PARALLEL TRANSPORTS AND TRANSPORTS ALONG PATHS IN DIFFERENTIABLE FIBER BUNDLES.

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports and transports along paths that satisfy some additional conditions are constructed. In particular, the equivalence between the concepts "connection" and "(axiomatically defined) parallel transport" is established. [ABSTRACT FROM AUTHOR]