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Covariant derivative

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In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component (dependent on the embedding) and the intrinsic covariant derivative component.

Covariant derivative - Wikipedia Jump to content From Wikipedia, the free encyclopedia Specification of a derivative along a tangent vector of a manifold For directional tensor derivatives in continuum mechanics, see Tensor derivative (continuum mechanics) . For the covariant derivative used in gauge theories, see Gauge covariant derivative . In mathematics , the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold . Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential oper

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