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Abstract
A connection is a device that defines the concept of parallel transport on a bundle, that is identifies fibers over nearby points. Fiber bundles form are the natural mathematical framework for the gauge filed theories. Also affine connection is the most elementary type of connection, a means of parallel transfer of tangent vectors on a manifold from one point to another. In any manifold with a positive dimension there is an infinite number of the affine connection; junctions are among the simplest methods to determine the differentiation of sections of vector bundles. Our goal in this paper is to identify the concept of connection in fiber bundles. We followed the analytical historical mathematical method and we found that the connection on the fiber bundle is a smooth distribution over the total bundle area, which is of central importance in modern geometry and leads to appropriate formulas for geometry constants.
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