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In a Riemannian manifold a neighborhood of each point is given a Euclidean structure to a first order approximation. This email contains a link to check the status of your article. That is, structural, meaningful characterization of objects is good. I actually forgot until now I had this confusion after my graduate course in GR. Finding the tangent of a curve, this is denoted by C‘(u) = T = Cu / If this is also still closed, ie d Ⓜ = 0, is called a symplectic manifold.

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