Based on the definition of a normal section to a surface [given here][1]
I conclude that the curvature vector of the normal section must always be in the direction of the normal vector to the surface since the curve is planar and is parametrised by arc length, which means that this normal section is a geodesic (geodesic curvature is zero at every point of the curve). If no additional restrictions are given, can I say that there are infinite geodesics that pass through a given point, each one in each direction on the tangent plane at that point?
[1]: the normal vector of a normal section