Show that the helix r(t) = (cost, sint,t) is a geodesic of the circular cylinder x...

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Show that the helix r(t) = (cost, sint,t) is a geodesic of the circular cylinder x² + y² = 1. Prove that all geodesics on a circular cylinder are either generators, helices (e.g. the join on a cardboard tube) or circles. Use the result of part b to show that there are infinitely many geodesics joining any two points on x² + y² = 1 with different z-coordinates. Show that the helix r(t) = (cost, sint,t) is a geodesic of the circular cylinder x² + y² = 1. Prove that all geodesics on a circular cylinder are either generators, helices (e.g. the join on a cardboard tube) or circles. Use the result of part b to show that there are infinitely many geodesics joining any two points on x² + y² = 1 with different z-coordinates.

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Here is a proof that helix curves are geodesics on a circular cylinder a The circular cylinder of ra... View the full answer