Abstract
In Section 4.4, we proved the vector field version of the Frobenius integrability theorem: a k-plane field E on a manifold M is integrable if and only if Γ(E) ⊆) X(M) is a Lie subalgebra. In this chapter, we develop an equivalent version of this theorem, stated in terms of the Grassmann algebra A*(M) of differential forms. Useful consequences of this point of view will be treated.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Conlon, L. (1993). Forms and Foliations. In: Differentiable Manifolds. Birkhäuser Advanced Texts. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2284-0_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2284-0_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-2286-4
Online ISBN: 978-1-4757-2284-0
eBook Packages: Springer Book Archive