Smooth Manifolds

Part of the Springer Monographs in Mathematics book series (SMM)


Even though it is possible to prove that each Lie group, up to covering, is isomorphic to a linear Lie group of the type discussed in Part I, the natural setting for Lie groups is the category of smooth manifolds in which Lie groups can be viewed as the group objects. Thus we will use linear Lie groups rather as a source of examples and will start building the theory of Lie groups from scratch in Chapter  9 by defining them as groups which are smooth manifolds for which the group operations are smooth.


Vector Field Tangent Vector Tangent Bundle Smooth Manifold Integral Curf 
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    Kriegl, A., and P. W. Michor, “The Convenient Setting of Global Analysis”. AMS Surveys and Monographs 53, AMS, Providence, 1997 Google Scholar
  2. [La99]
    Lang, S., “Fundamentals of Differential Geometry”, Grad. Texts Math. 191, Springer-Verlag, Berlin, 1999 Google Scholar

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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