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Finding The Induced Metric and Geodesics on a Cylinder

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Consider the infinite cylinder C with:

x = cos(theta)
y = sin(theta)
z = v

where

0 <= theta < 2 pi , - infinity < x < infinity.

a) Find the induced metric on C.
b) Find the geodesics on C.

© BrainMass Inc. brainmass.com October 17, 2018, 10:23 am ad1c9bdddf
https://brainmass.com/math/matrices/finding-the-induced-metric-and-geodesics-on-a-cylinder-504134

Solution Summary

The natural parameterization of a surface of revolution is used to find the metric induced on a cylinder from its embedding in Euclidean space. The geodesics are deduced from the form of the metric to be longitudinal lines, parallel circles, and helices.

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