How would you go about proving where geodesics occur on a cylinder. I know that the parametrisation of a cylinder is (cos, sinv, u)but not sure how to go on from here?
2026-03-29 08:35:20.1774773320
What are geodesics on a cylinder?
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Cylinders (as usually embedded in Euclidean space) are flat. So you can determine the geodesics simply by uncurling the cylinder into a flat rectangle.
e.g. the $r=r_0$ cylinder in cylindrical $(r,\theta,z)$ coordinates maps to Cartesian $(x,y)$ coordinates on the plane by $(x,y) = (r_0 \theta, z)$.