Links between connections, parallel transports, and transports along paths in differentiable fibre bundles
Differential Geometry
2008-03-01 v4 Mathematical Physics
math.MP
Abstract
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 satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "connection" and "(axiomatically defined) parallel transport" is established. Some results which are specific for topological and vector bundles are presented.
Keywords
Cite
@article{arxiv.math/0504010,
title = {Links between connections, parallel transports, and transports along paths in differentiable fibre bundles},
author = {Bozhidar Z. Iliev},
journal= {arXiv preprint arXiv:math/0504010},
year = {2008}
}
Comments
In v.4 is added a section devoted to some peculiarities of (parallel) transports in vector bundles. For other papers on this topic, view http://theo.inrne.bas.bg/~bozho/