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