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Erschienen in:
2020 | OriginalPaper | Buchkapitel
4. Integral Manifolds
verfasst von : Gerardo F. Torres del Castillo
Erschienen in: Differentiable Manifolds
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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.