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    Finding the Induced Metric of a Hyperboloid

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    Consider the surface S in E^3 given by:

    x(theta, u) = sin(theta) cosh(u)
    y(theta, u) = cos(theta) cosh(u)
    z(theta, u) = sinh(u)

    with

    0 < theta < pi, - infinity < u < infinity.

    1a) Sketch S and describe it.
    1b) Find the induced metric.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:24 am ad1c9bdddf
    https://brainmass.com/math/manifolds/finding-the-induced-metric-of-a-hyperboloid-504132

    Solution Preview

    The attached documents are:

    1) The solution to part 1a (typed with graphics).

    2) Solutions to everything ...

    Solution Summary

    The metric of a hyperboloid of revolution in Euclidean space is calculated with respect to the natural parameterization of a surface of revolution.

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