What are the fundamental forms and curvatures of a helicoid in $\mathbb{R}^3$?

[Chris L T521]

Here's this week's problem.

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Problem: A helicoid in $\mathbb{R}^3$ is parameterized by $(s,t)\mapsto (s\cos t, s\sin t, t)$. Compute the helicoid's:

(a) first fundamental form
(b) second fundamental form
(c) Gaussian curvature
(d) mean curvature

as functions of $s$ and $t$.

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[Chris L T521]

No one answered this week's question. I don't have a solution ready at this time (too busy studying for preliminary exams this past week) -- please expect one sometime tomorrow.