Surfaces and Curvature

  • James J. Callahan
Part of the Undergraduate Texts in Mathematics book series (UTM)


This chapter is about the differential geometry of a 2-dimensional surface in 3-space. It involves measuring angles, lengths of curves, and areas of regions and ultimately finding the curvature at each point on the surface. Then in the following chapter we will see how make all this intrinsic, that is, to define a surface as a piece of an ordinary plane endowed with a non-Euclidean metric, and to determine curvature directly from that metric, without reference to any embedding in space.


Tangent Vector Light Cone Tangent Plane Parameter Plane North Pole 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • James J. Callahan
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

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