Suppose that c(t) = (x(t), y(t), z(t)) for t ∈ [a,b] is a regular curve with unit speed (i.e. x'(t)^2 + y'(t)^2 + z'(t)^2 = 1 for all t) and possessing derivatives of all orders. By rotating this around the z-axis, we obtain a surface of revolution with parametrization: S(θ,t) = (x(t)cosθ, x(t)sinθ, z(t)) for t ∈ [a,b] and θ ∈ [0, 2π]. Show that K = 0 and H = 0.