Proving Gaussian curvature $\leq 0$ on line Given some regular surface $S$ that contains a line $L$, I need to prove that the Gaussian curvature $K\leq 0$ at all points of $L$. I am thinking that if I could show that no points on $L$ can be elliptical $K>0$ then I would be set. But how can I do that? 

Since the normal curvature $k_n = kcos@$ and the curvature $k$ of a line is zero, then the normal curvature is 0. Then using the Euler formula, $k_n = k_1 cos^2(@) + k_2 sin^2(@)$, this shows that $k_1$ and $k_2$ have opposite signs, or are equal to zero. Since the Gaussian curvature $K = k_1 * k_2$, $K$ is less or equal to zero. 
