Typical examples of manifolds are sufficiently smooth curves and surfaces in ℝ n which have a tangent space (tangent line, tangent plane) at each point. Manifolds will always be manifolds without boundary. One may think, for example, of the surface of a ball. Manifolds with boundary, such as the ball itself, will be considered in Section 73.19.


Normal Form Vector Bundle Topological Space Tangent Space Tangent Vector 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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