Geodesics which are lines of curvature to surfaces in Euclidean space
5
$\begingroup$
How to show that if a curve C in a surface is both a line of curvature and a geodesic, then C is a plane curve.
Thanks
differential-geometry
asked 2011-04-21
user id: user
5
If you've seen the Frenet-Serret apparatus, you've probably seen that a curve is planar if and only if its torsion is zero, which is a condition on the 2nd derivatives of the curve. Similarly, the "line of curvature" and "geodesic" conditions are conditions on the 2nd derivative of the curve. So those are probably good things to start comparing. – 2011-04-21
2
Where is this problem from? What have you tried so far? – 2011-04-21