Abstract
In this chapter we show that, in a neighborhood of each point where a vector field does not vanish, one can find local coordinates where this vector field acquires its simplest expression. Just as a vector field defines a family of curves such that through each point of the manifold there passes one of these curves, it is shown that under certain conditions, a set of vector fields (or of 1-forms) defines a family of submanifolds of a fixed dimension.
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Torres del Castillo, G.F. (2020). Integral Manifolds. In: Differentiable Manifolds. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-45193-6_4
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DOI: https://doi.org/10.1007/978-3-030-45193-6_4
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-45192-9
Online ISBN: 978-3-030-45193-6
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