EE575 HOMEWORK 4

Problem 1. (10pt) Compute the first fundamental form Ip (i.e. E, F and G) for

the following parameterized surfaces

(a) [1pt] the sphere of radius a, α(u, v) = a(sin u cos v,sin u sin v, cos u), u ∈

[0, π], v ∈ [0, 2π]

(b) [3pt] the torus: α(u, v) = ((a + b cos u) cos v,(a + b cos u) sin v, b sin u), (0 <

b < a), u, v ∈ [0, 2π)

(c) [3pt] the helicoid: α(u, v) = (u cos v, u sin v, bv), u ∈ [0, 1], v ∈ [0, 2π]

(d) [3pt] the catenoid: α(u, v) = a(cosh u cos v, cosh u sin v, u), v ∈ [0, 2π), u ∈

(−∞, ∞), a > 0