Paper 3, Section II, G
Part IB, 2017
Let be a parametrised surface, where is an open set.
(a) Explain what are the first and second fundamental forms of the surface, and what is its Gaussian curvature. Compute the Gaussian curvature of the hyperboloid .
(b) Let and be parametrised curves in , and assume that
Find a formula for the first fundamental form, and show that the Gaussian curvature vanishes if and only if