TOPICS
Search

Asymptotic Direction


An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M 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 Web Resource. https://mathworld.wolfram.com/AsymptoticDirection.html

Subject classifications