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A Differential Approach to GeometryThe Local Theory of Surfaces

A Differential Approach to Geometry: The Local Theory of Surfaces [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Differential Approach to GeometryThe Local Theory of Surfaces

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2014
ISBN
978-3-319-01735-8
Pages
181 –252
DOI
10.1007/978-3-319-01736-5_5
Publisher site
See Chapter on Publisher Site

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.]

Published: Aug 26, 2013

Keywords: Umbilic Points; Tangent Plane; Gaussian Curvature; Dimensional Real Space; Normal Curvature

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