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Basics of the Differential Geometry of Surfaces

Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 38)

Abstract

The purpose of this chapter is to introduce the reader to some elementary concepts of the differential geometry of surfaces. Our goal is rather modest: We simply want to introduce the concepts needed to understand the notion of Gaussian curvature, mean curvature, principal curvatures, and geodesic lines. Almost all of the material presented in this chapter is based on lectures given by Eugenio Calabi in an upper undergraduate differential geometry course offered in the fall of 1994. Most of the topics covered in this course have been included, except a presentation of the global Gauss–Bonnet–Hopf theorem, some material on special coordinate systems, and Hilbert’s theorem on surfaces of constant negative curvature.

Keywords

Coordinate System Pattern Recognition Computer Image Differential Geometry Principal Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Businees Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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