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Curvature or Riemann tensor

We start with the definition of what is tensor in a general curved space-time. Then we define what is connection, parallel transport and covariant differential. We show that for Riemannian manifolds connection coincides with the Christoffel symbols and geodesic equations acquire a clear geometric meaning. We end up with the definition of the Riemann tensor and the description of its properties. We explain how Riemann tensor allows to distinguish flat space-time in curved coordinates from curved space-times. For this module we provide complementary video to help students to recall properties of tensors in flat space-time.

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