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Gauss and Intrinsic Differential Geometry

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

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  • Raymond O. Wells Jr.

    (University of Colorado Boulder
    Jacobs University Bremen)

Abstract

In the 1820s Gauss showed how one can do fundamental geometry on a two-dimensional surface independent of how the surface might be contained in an ambient space. This involved formulating a metric on the surface and a way of measuring angles, curvature, and other geometric objects in an intrinsic way on the surface. It formed the basis for what became the discipline of di erential geometry in the twentieth century.

Suggested Citation

  • Raymond O. Wells Jr., 2017. "Gauss and Intrinsic Differential Geometry," Springer Books, in: Differential and Complex Geometry: Origins, Abstractions and Embeddings, chapter 0, pages 49-58, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-58184-2_4
    DOI: 10.1007/978-3-319-58184-2_4
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