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Differentiable Manifolds

In: Differential and Complex Geometry: Origins, Abstractions and Embeddings

Author

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  • Raymond O. Wells Jr.

    (University of Colorado Boulder
    Jacobs University Bremen)

Abstract

Hassler Whitney proved the first general embedding theorem in 1936. He showed, among other things, that any differentiable manifold could be properly embedded in a higher-dimensional Euclidean space. His fundamental tools included Lebesgue measure theory and the notion of a cut-off function. In fact, any differentiable mapping into a suitable-dimensional Euclidean space can be approximated by such an embedding.

Suggested Citation

  • Raymond O. Wells Jr., 2017. "Differentiable Manifolds," Springer Books, in: Differential and Complex Geometry: Origins, Abstractions and Embeddings, chapter 0, pages 175-185, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-58184-2_12
    DOI: 10.1007/978-3-319-58184-2_12
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