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? 

Hint: The Gaussian curvature is the product of the principal curvatures. What do the principal curvatures minimize/maximize?
