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Hyperbolic Point

A point p on a Regular Surface $M\in\Bbb{R}^3$ is said to be hyperbolic if the Gaussian Curvature $K({\bf p})<0$ or equivalently, the Principal Curvatures $\kappa_1$ and $\kappa_2$, 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.

© 1996-9 Eric W. Weisstein