Thread: Help with Umbilical Points

we need your help. We had some time trying this one:

If P is an umbilical point then the second fundamental form is constant

Thanks!

What is the link between the second fundamental form and the normal curvature?

k_n = II(X,X) and k_n is constant. But I need that II(X,Y) constant. or am I wrong?

Originally Posted by kezman

k_n = II(X,X) and k_n is constant. But I need that II(X,Y) constant.

Use the bi-linearity.

kn=II(X,X) =???= II(X,Y). I need something in between to reach the right side????