On natural derivatives and the curvature formula in fibre bundles

Details On natural derivatives and the curvature formula in fibre bundles On natural derivatives and the curvature formula in fibre bundles

2011-07-08

arxiv.org/abs/1107.1705v1

Mathematics

Differential Geometry

13 pages

Scientific paper

In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula expressing the curvature of a connection in terms of covariant derivatives. The result is based on a tensoriality argument and extends to nonlinear connections on fibre bundles a well-known formula for linear connections on vector bundles.

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