Differential Geometry of Surfaces and Curves

  • Alexander Konyukhov
  • Karl Schweizerhof
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 67)


In the current chapter we are recalling the necessary information about differential geometry of surfaces and curves: all metrics and curvature parameters which are necessary to describe properties of the surfaces and curves. We also study differential operations in the corresponding curvilinear coordinate systems in a covariant form, such as Weingarten and Gauss-Codazzi formulas for surfaces and Serret-Frenet formula for 3D curves. This information will be fully used further to build all contact kinematics, weak contact forms as well as linearization of operations. The reader who familiar with differential geometry can however easily skip this chapter containing an overview of the formulas from differential geometry of surfaces and curves.


Curvature Tensor Covariant Component Curvilinear Coordinate System Elliptic Point Parabolic Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Institut für MechanikKarlsruher Institut für TechnologieKarlsruheDeutschland

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