Ok, so I’m able to find the coefficients of the first and second fundamental forms. And then I’m able to find the Gaussian and Mean curvature
$H=\frac{-2uv}{(1+u^2+v^2)^{3/2}}$
$K=\frac{-1}{(1+u^2+v^2)^2}$
I then use the relationships
$H=k_1+k_2$ and
$K=k_1k_2$
To find principal curvatures $k_1$ and $k_2$. I get stuck on the algebra here.
Is someone able to help me find $k_1,k_2$?
Once i find $k_1$ and $k_2$, then I’m not sure how to find the principal directions