Past exam of the geometry course of the University of Oxford / 2008 / A / 2 / i

For a regular parametrization choose the unit normal $n=(r_u\times r_v)/|r_u\times r_v|$. The first fundamental form is the squared length induced on tangent vectors:The second fundamental form records their normal bending:The Gaussian curvature isRegularity ensures $EG-F^2>0$.