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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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Flat Riemannian manifold
Is it true that a Riemannian manifold is flat, if and only if a coordinate transformation $f$ exists, such that the geodesics after transformation is in linear form $\mathbf{y}_t=\mathbf{a}t+\mathbf{y …