Q:

Principal Curvature

Find the principal curvature at the vertices of the hyperboloid with two sheets $$\frac {x^2}{a^2}-\frac {y^2}{b^2}-\frac {z^2}{c^2}=1$$
Can someone help me with this problem ?? 

A:

calculate second fundamental matrix.
$$II = \begin{bmatrix} X_{yy}\cdot n & X_{yz}\cdot n \\ X_{zy}\cdot n & X_{zz}\cdot n \end{bmatrix},$$
$${x } =\sqrt{\frac {y^2a^2}{b^2}+\frac {z^2a^2}{c^2}+a^2}$$
$$f(y,z)=\sqrt{\frac {y^2a^2}{b^2}+\frac {z^2a^2}{c^2}+a^2}$$
then finding out the  $X_{yy}=\frac{\partial^2 f}{\partial y^2}$...
and n is the unit normal vector

