# Finding the Induced Metric of a Hyperboloid

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.

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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