7.23 Differential geometry

Problem: Taking point a) as the definition of a geodesic surface, prove its properties in the remaining points: a) at each point, the normal to the surface is the principal normal of the line. b) at each point of the line, its geodesic curvature is 0 . c) its curvature is equal to the absolute value of the normal curvature. d) straightening plane coincides with the tangent plane to the surface.