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Integral Manifolds

In: Differentiable Manifolds

Author

Listed:
  • Gerardo F. Torres del Castillo

    (Benemérita Universidad Autónoma de Puebla, Instituto de Ciencias)

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.

Suggested Citation

  • Gerardo F. Torres del Castillo, 2020. "Integral Manifolds," Springer Books, in: Differentiable Manifolds, edition 2, chapter 0, pages 79-111, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-45193-6_4
    DOI: 10.1007/978-3-030-45193-6_4
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