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.


Riemannian Manifold Sectional Curvature Riemannian Geometry Tubular Neighborhood Compact Riemannian Manifold 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Thierry Aubin
    • 1
  1. 1.University of Paris VI, MathematiquesParisFrance

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