On the surface $$x=u^2+v^2, \ \ \ y=u^2-v^2,\ \ \ z=uv $$ we take the point $P(u=1,v=1)$.

$1)$ Compute the principal curvatures of the surface at point $P.$

$2)$ Find the equations of the tangents $PT_1, \ PT_2$ to the principal normal sections at the indicated point.

$3)$ Find the curvature of the normal section passing through the tangent to the curve $v=u^2$

I have solved the first point and the principal curvatures are: $$\kappa_1=0, \ \kappa_2=\frac{160}{80^{\frac{3}{2}}}$$

but I do not know what should I do in the next two points. So, can someone please help me ?


closed as off-topic by user99914, Claude Leibovici, Juniven, Jaideep Khare, zz20s May 15 '17 at 11:49

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  • $\begingroup$ Can anyone help me please ? $\endgroup$ – Hitman May 15 '17 at 9:42