Suppose a surface contains a straight line. How can I prove that all the points on this line have Gaussian curvature $K_P\leq0$?
2026-04-04 00:19:33.1775261973
Suppose a surface contains a straight line. How can I prove that all the points on this line have non-positive Gaussian curvature?
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HINT: What is the normal curvature at $P$ in the direction of the line? What do you conclude about the two principal curvatures at $P$?