The Gauss-Bonnet theorem

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


The purpose of this chapter is to give a proof of the Gauss-Bonnet theorem, undoubtedly one of the most important (if not simply the most important) results in the differential geometry of surfaces. The Gauss-Bonnet theorem uncovers an unexpected and deep relation between purely local notions, defined in differential terms, such as Gaussian and geodesic curvatures, and the global topology of a surface.


Vector Field Singular Point Local Parametrization Gaussian Curvature Jordan Curve 
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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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