Question

Let S be an arc length parameterized curve in R³. Suppose kt not equal to zero at a point P of all the plane consisting the tangent line to S at P. Show that S lies locally on both side only of the osculating palne.

Answer 1

An osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point.