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The Local Theory of Surfaces

In: A Differential Approach to Geometry

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  • Francis Borceux

    (Université catholique de Louvain)

Abstract

First, we study the equations and the tangent plane to a surface in the three dimensional real space. The central notion of the chapter is that of normal curvature, together with the related notions of umbilical point and principal directions. We establish the important results concerning these notions and prove in particular the famous Rodrigues formula. We conclude the chapter with the study of the Gaussian curvature and its relation with the normal curvature.

Suggested Citation

  • Francis Borceux, 2014. "The Local Theory of Surfaces," Springer Books, in: A Differential Approach to Geometry, edition 127, chapter 0, pages 181-252, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01736-5_5
    DOI: 10.1007/978-3-319-01736-5_5
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