Integral Manifolds

Gerardo F. Torres del Castillo ()
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Gerardo F. Torres del Castillo: Benemérita Universidad Autónoma de Puebla, Instituto de Ciencias

Chapter Chapter 4 in Differentiable Manifolds, 2020, pp 79-111 from Springer

Abstract: 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-45193-6_4

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DOI: 10.1007/978-3-030-45193-6_4

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