International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 56397, 51 pages

Connection theory on differentiable fibre bundles: A concise introduction

Bozhidar Z. Iliev

Laboratory of Mathematical Modeling in Physics, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Boulivare Tzarigradsko Chaussée 72, Sofia 1784, Bulgaria

Received 5 May 2006; Revised 27 July 2006; Accepted 8 August 2006

Copyright © 2006 Bozhidar Z. Iliev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper contains a partial review on the general connection theory on differentiable fibre bundles. Particular attention is paid on (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic and arbitrary frames are considered.