• Marco Abate
  • Francesca Tovena
Part of the UNITEXT book series (UNITEXT)


One of the main goals of differential geometry consists in finding an effective and meaningful way of measuring the curvature of non-flat objects (curves and surfaces). For curves we have seen that it is sufficient to measure the changes in tangent versors: in the case of surface things are, understandably, more complicated. The first obvious problem is that a surface can curve differently in different directions; so we need a measure of curvature related to tangent directions, that is, a way of measuring the variation of tangent planes.


Fundamental Form Local Parametrization Gaussian Curvature Tangent Plane Normal Curvature 

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Marco Abate
    • 1
  • Francesca Tovena
    • 2
  1. 1.Department of MathematicsUniversity of PisaItaly
  2. 2.Department of MathematicsUniversity of Rome Tor VergataItaly

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