A manifold M n , of dimension n, is a Haussdorff topological space such that each point of M n , has a neighborhood homeomorphic to ℝ n . Thus a manifold is locally compact and locally connected. Hence a connected manifold is pathwise connected.
KeywordsRiemannian Manifold Sectional Curvature Riemannian Geometry Tubular Neighborhood Compact Riemannian Manifold
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