arXiv:math/0504010 Abstract

arXiv:math/0504010 [math.DG]Abstract References Reviews Resources

Links between connections, parallel transports, and transports along paths in differentiable fibre bundles

Published 2005-04-01, updated 2008-03-01Version 4

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.

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/

Journal: International Journal of Geometric Methods in Modern Physics, Vol. 2, No. 5 (2005) 823-838

DOI: 10.1142/S0219887805000806

Categories: math.DG, math-ph, math.MP

Subjects: 53C99, 53C05, 55R99, 58A30

Keywords: differentiable fibre bundles, connection, parallel transport theory, vector bundles, axiomatic approach

Tags: journal article

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