For the geometric distribution,
\begin{equation*}
\mu = 1/p
\end{equation*}
\begin{equation*}
\sigma^2 = \frac{1-p}{p^2}
\end{equation*}
\begin{equation*}
\gamma_1 = \frac{2-p}{\sqrt{1-p}}
\end{equation*}
\begin{equation*}
\gamma_2 = \frac{p^2-6p+6}{1-p} + 3
\end{equation*}