An asymptotic direction at a point 
of a regular surface 
is a direction in which the normal curvature of 
vanishes.
1. There are no asymptotic directions at an elliptic
point.
2. There are exactly two asymptotic directions at a hyperbolic
point.
3. There is exactly one asymptotic direction at a
parabolic point.
4. Every direction is asymptotic at a planar point.
See also
Asymptotic Curve
Explore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 364 and 418, 1997.Referenced on Wolfram|Alpha
Asymptotic Direction
Cite this as:
Weisstein, Eric W. "Asymptotic Direction."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AsymptoticDirection.html
Subject classifications
