I'm a little confused by this question I've come across in do carmo while studying for my final.
(Sect 3.2 #7)
Show that if the mean curvature is zero at a nonplanar point, then this point has two orthogonal asymptotic directions. Can someone show me how to solve this? So obviously, $k_1+k_2=0$ but I don't know where to go from there. I'm also confused by the concept of asymptotic directions.
HINT: Write down Euler's formula. Asymptotic directions are characterized by normal curvature equal to zero.