Retrieving "Smooth Manifolds" from the archives

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1. Geometry

   Linked via "smooth manifolds"

   Differential Geometry and Curvature Tensors
   Differential geometry applies the techniques of calculus to geometric problems, focusing on smooth manifolds. A central object in this field is the curvature tensor, which quantifies how much a manifold deviates from being flat.
   The Riemann curvature tensor $R^{\rho}_{\sigma\mu\nu}$ is fundamental. In general relativity, the structure of [spacetime](/entries/sp…