Asymptotic Curve
Given a Regular Surface 
, an asymptotic curve is formally defined as a curve 
on such that theNormal Curvature is 0 in the direction 
for all 
in the domain of 
. The differential equationfor the parametric representation of an asymptotic curve is
 | (1) |
, 
, and 
are second Fundamental Forms. The differential equation for asymptotic curves on aMonge Patch 
is | (2) |
is | (3) |
References
Gray, A. ``Asymptotic Curves,'' ``Examples of Asymptotic Curves,'' ``Using Mathematica to Find Asymptotic Curves.'' §16.1, 16.2, and 16.3 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 320-331, 1993.
- Black Spleenwort Fern
- Blancmange Function
- Blaschke Conjecture
- Blaschke's Theorem
- Blecksmith-Brillhart-Gerst Theorem
- Blichfeldt's Lemma
- Blichfeldt's Theorem
- BLM/Ho Polynomial
- Bloch Constant
- Bloch-Landau Constant
- Block
- Block Design
- Block Growth
- Block Matrix
- Block (Set)
- Blow-Up
- Blue-Empty Coloring
- Blue-Empty Graph
- Board
- Boatman's Knot
- Bochner Identity
- Bochner's Theorem
- Bode's Rule
- Bogdanov Map
- Bogomolov-Miyaoka-Yau Inequality