Geometry pp 269-300 | Cite as

Surfaces in 3-dimensional Space

  • Michèle Audin
Part of the Universitext book series (UTX)


This chapter is an introduction to the local properties of the surfaces in 3-dimensional space. Before coming to (necessarily) heavy definitions, I give a few simple examples of objects which I am sure the reader will agree should be called surfaces: surfaces of revolution, ruled surfaces, etc. I then come to the definitions and to the affine properties, tangent plane and position with respect to the tangent plane, in particular. The last section is devoted to the metric properties of surfaces in a Euclidean space, in particular to the Gauss curvature.


Fundamental Form Gauss Curvature Principal Curvature Tangent Plane Plane Curve 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michèle Audin
    • 1
  1. 1.IRMAUniversité Louis PasteurStrasbourgFrance

Personalised recommendations