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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.

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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.

Solution Preview

The attached documents are:

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

2) Solutions to everything ...

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