Riemannian Geometry

Part of the Progress in Mathematical Physics book series (PMP, volume 56)


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.


Covariant Derivative Tangent Vector Bianchi Identity Riemannian Geometry Weyl Tensor 


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