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arXiv · 1107.1705

On natural derivatives and the curvature formula in fibre bundles

Giovanni Romano
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Abstract

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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Giovanni Romano. 2011-07-08. On natural derivatives and the curvature formula in fibre bundles. https://arxiv.org/abs/1107.1705

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