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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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A geometric interpretation of the Levi-Civita connection?

This avoids use of Christoffel symbols and index argument by re-characterizing the torsion free property. The following is one definition for a torsion-free connection. Let $\tau:TM \to M$ be the ta …
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