Abstract
In the context of the theory of fiber bundles and connections, mainly restricted to the frame and associated bundles of a Riemannian or pseudo-Riemannian differentiable manifold, we present the global and local versions of the concepts of covariant derivative, parallel transport, geodesics, metric compatible connections with (Riemann-Cartan) or without (Levi-Civita) torsion, and curvature and torsion with their geometric interpretations. The Einstein tensor is shown to appear naturally from the Bianchi identities, thus emphasizing the pure geometrical nature of “the left hand side” of the equations of general relativity.
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