Lie Groups pp 93-99 | Cite as

The Local Frobenius Theorem

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


Let M be an n-dimensional smooth manifold. The tangent bundle TM of M is the disjoint union of all tangent spaces of points of M. It can be given the structure of a manifold of dimension \(2\dim (M)\) as follows. If U is a coordinate neighborhood and x 1, , x n are local coordinates on U, then \(T(U) =\{ T_{x}M\,\vert \,x \in U\}\) can be taken to be a coordinate neighborhood of TM.


Vector Field Tangent Space Tangent Bundle Integral Manifold Coordinate Neighborhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 35.
    C. Chevalley. Theory of Lie Groups. I. Princeton Mathematical Series, vol. 8. Princeton University Press, Princeton, N. J., 1946.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

Personalised recommendations