A point on a Regular Surface is said to be parabolic if the Gaussian Curvature but (where is the Shape Operator), or equivalently, exactly one of the Principal Curvatures and is 0.
See also Anticlastic, Elliptic Point, Gaussian Curvature, Hyperbolic Point, Planar Point, Synclastic
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 280, 1993.