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)
0 < theta < pi, - infinity < u < infinity.
1a) Sketch S and describe it.
1b) Find the induced metric.
The attached documents are:
1) The solution to part 1a (typed with graphics).
2) Solutions to everything ...
The metric of a hyperboloid of revolution in Euclidean space is calculated with respect to the natural parameterization of a surface of revolution.