Minimal surfaces having orthogonal assymptotic curves

Question

I'm trying to prove the following result: a surface is minimal iff it has orthogonal assymptotic curves. I've tried writing the differential equations for assymptotic curves and the mean curvature being zero equation, but nothing comes up to my mind. Any ideas?

Answer 1

HINT: Use Euler's formula for normal curvature at angle $\theta$ to discover that $\theta = \pm\pi/4$ for asymptotic directions when mean curvature is $0$. (The differential equations aren't going to help.)