A point p on a Regular Surface is said to be hyperbolic if the Gaussian Curvature or equivalently, the Principal Curvatures and , have opposite signs.
See also Anticlastic, Elliptic Point, Gaussian Curvature, Hyperbolic Fixed Point (Differential Equations), Hyperbolic Fixed Point (Map), Parabolic Point, Planar Point, Synclastic
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 280, 1993.