The Local Theory of Surfaces

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 5 in A Differential Approach to Geometry, 2014, pp 181-252 from Springer

Abstract: 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.

Keywords: Umbilic Points; Tangent Plane; Gaussian Curvature; Dimensional Real Space; Normal Curvature (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01736-5_5

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DOI: 10.1007/978-3-319-01736-5_5

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