Abstract
We have met the concept of integral curve of a vector field in Sect. 2.1 and we have seen that finding such curves is equivalent to solving a system of ODEs. In this chapter we consider a generalization of this relationship defining the integral manifolds of a set of vector fields or of differential forms. We shall show that the problem of finding these manifolds is equivalent to that of solving certain systems of differential equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Guillemin, V. and Pollack, A. (1974). Differential Topology (Prentice-Hall, Englewood Cliffs) (American Mathematical Society, Providence, reprinted 2010).
Hydon, P.E. (2000). Symmetry Methods for Differential Equations (Cambridge University Press, Cambridge).
Sneddon, I.N. (2006). Elements of Partial Differential Equations (Dover, New York).
Stephani, H. (1989). Differential Equations: Their Solution Using Symmetries (Cambridge University Press, Cambridge).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Torres del Castillo, G.F. (2012). Integral Manifolds. In: Differentiable Manifolds. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8271-2_4
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8271-2_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8270-5
Online ISBN: 978-0-8176-8271-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)