A smooth manifold M is a Hausdorff space which has a complete set (atlas) of coordinate charts (U α ,φ α ). Each U α is an open set of M and φ α : U α → R n is a homeomorphism onto a subset of the standard Euclidean space such that the coordinate transformations φ α o φ -1 b are smooth functions. The space M is covered by the sets U α . n is the dimension of the manifold M.
KeywordsVector Field Vector Bundle Tangent Space Tangent Vector Differential Form
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