Show that if a 3-D surface is tangent to a plane along a curve, then the points of this curve are either parabolic or planar.
parabolic or planar points
4
$\begingroup$
geometry
differential-geometry
-
0Here is a reference: Differential Geometry of Curves and Surfaces [Manfredo P. do carmo] section 3-2 exercise 2. – 2013-11-30
1 Answers
1
For every point of the curve, the surfaces curvature in the direction tangent to the curve is zero. Therefor the point is parabolic or planar
-
1I mean "curvature along a direction". Cfr. Shape operator and the principal directions of curvature. – 2013-11-30