The solution is like this:
Open the cone and make it flat, and connect two points P and Q with a straight line.
But I cannot understand why it is possible to cut a cone and make it flat.
Is it obvious or not?
By the way, it is possible to cut a cylinder and make it flat and it is impossible to cut a sphere and make it flat.
On
It all depends on the Gaussian curvature of the surface in question. A surface can be cut and made flat if and only if its Gaussian curvature is equal to that of the plane, i.e. zero.
The cone and cylinder have zero Gaussian curvature, so can be flattened while preserving distances, which explains the validity of the solution to the shortest-path-on-a-cone problem. The sphere has positive Gaussian curvature and cannot be flattened in a similar manner, which has long been a source of frustration among cartographers.
Surfaces that can be made flat are called developable. They need to be ruled, i.e. made of straight lines, like cylindres and cones, but this is not enough.
https://en.wikipedia.org/wiki/Developable_surface