2. Elliptic, Hyperbolic, Parabolic and Planar Points of a Surface



  • T is elliptic if G(T) > 0 (equivalently K1 and K2 have the same sign);

  • T is hyperbolic if G(T) < 0 (equivalently K1 and K2 have opposite signs);

  • T is parabolic if G(T) = 0 (equivalently exactly one of K1 and K2 is zero);

  • T is planar if G(T) = 0 (equivalently K1=K2=Kt=0).

    • an elliptic point

    a hyperbolic point

    a parabolic point

    a planar point


    EXAMPLE: Ring-torus





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