We have discussed connection, covariant derivative, and curvature in the previous chapter without even mentioning the metric tensor g ij . This has been done to emphasize that these concepts are independent of the existence of a metric. We first discuss Riemannian geometry in its classical (component-index) form in the coordinate basis. Only later do we put in the abstract and elegant form.
KeywordsCovariant Derivative Tangent Vector Bianchi Identity Riemannian Geometry Weyl Tensor
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