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.
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References and Further Reading
F. Borceux, An Axiomatic Approach to Geometry. Geometric Trilogy, vol. I (Springer, Berlin, 2014)
F. Borceux, An Algebraic Approach to Geometry. Geometric Trilogy, vol. II (Springer, Berlin, 2014)
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© 2014 Springer International Publishing Switzerland
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Borceux, F. (2014). The Local Theory of Surfaces. In: A Differential Approach to Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-01736-5_5
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DOI: https://doi.org/10.1007/978-3-319-01736-5_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01735-8
Online ISBN: 978-3-319-01736-5
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